I need help within an hour! Exponential function

[JoshuaTree]

I'm a college sophmore, and this is the end of precalc/beginning of calc.

"My name is Leonard Smith, “Leaping Lennie” to my fans. I play college basketball where I am the star of my team. I have been offered a spot in the big leagues and I am very excited. I need your help.
Here are my two offers from the NBA team:


a) They will pay me a starting salary of $200,000 and will increase this salary by $40000 per year.
b) They will pay me a starting salary of $175000 and will increase my salary 25% per year.

Contracts on this team are renewed every 5 years.

My question is, which deal should I take and why?


assume that the points can be connected in a continuous line even if the account is only updated yearly, i.e., his salary is only revisited on a yearly basis during this 5 Year period and renegotiated completely after that). Then figure out which deal Lennie should take. Accumulated earnings should be taken into account."

I have no clue how to find the first function. I think it is 200,000^.25x. It might even be 200,000 (1 + .25/1)^1x, right? I am lost.
The second function is, I think, 175,000 x 1.125^x.
I have no idea what to do from here, other than compare the graphs to see which one pays more.

 

[Deleted member 4993]

"My name is Leonard Smith, “Leaping Lennie” to my fans. I play college basketball where I am the star of my team. I have been offered a spot in the big leagues and I am very excited. I need your help.
Here are my two offers from the NBA team:


a) They will pay me a starting salary of $200,000 and will increase this salary by $40000 per year.
b) They will pay me a starting salary of $175000 and will increase my salary 25% per year.


Contracts on this team are renewed every 5 years.


My question is, which deal should I take and why?


assume that the points can be connected in a continuous line even if the account is only updated yearly, i.e., his salary is only revisited on a yearly basis during this 5 Year period and renegotiated completely after that). Then figure out which deal Lennie should take. Accumulated earnings should be taken into account."

You should accept the deal that offers you most money in total at the end of five years (assuming no time-value of money).


You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...217#post322217


We can help - we only help after you have shown your work - or ask a specific question (not a statement like "Don't know any of these")

Please share your work with us indicating exactly where you are stuck - so that we may know where to begin to help you.

 

[JoshuaTree]

Fixed... Or at least I attempted to fix it.
If anyone could help me out before I leave for class at 11:40am Eastern time (currently 10:33am), I would truly be grateful. Even after 11:40am, feel free to reply.. I would like to understand this problem.

 

[Deleted member 4993]

"My name is Leonard Smith, “Leaping Lennie” to my fans. I play college basketball where I am the star of my team. I have been offered a spot in the big leagues and I am very excited. I need your help.
Here are my two offers from the NBA team:


a) They will pay me a starting salary of $200,000 and will increase this salary by $40000 per year.
b) They will pay me a starting salary of $175000 and will increase my salary 25% per year.


Contracts on this team are renewed every 5 years.


My question is, which deal should I take and why?


assume that the points can be connected in a continuous line even if the account is only updated yearly, i.e., his salary is only revisited on a yearly basis during this 5 Year period and renegotiated completely after that). Then figure out which deal Lennie should take. Accumulated earnings should be taken into account."

I have no clue how to find the first function. I think it is 200,000^.25x. It might even be 200,000 (1 + .25/1)^1x, right? I am lost.
The second function is, I think, 175,000 x 1.125^x.
I have no idea what to do from here, other than compare the graphs to see which one pays more.

You have not answered the question posed in "Read before Posting". Which grade are you in? What type of class is this (Math? Bus? Sports Management?). Please answer these with your reply to following question:

Anyway, the option (a) is growing by a constant amount ($40,000) everyear - the increase is not dependent on the present salary. This is not an exponential function - what type of function is this?

 

[HallsofIvy]

"My name is Leonard Smith, “Leaping Lennie” to my fans. I play college basketball where I am the star of my team. I have been offered a spot in the big leagues and I am very excited. I need your help.
Here are my two offers from the NBA team:


a) They will pay me a starting salary of $200,000 and will increase this salary by $40000 per year.

The first year is $200,000, the second year is 200,000+ 40000= $240000, the third year is 240000+ 40000= 200000+ 2(40000)= $280000, etc. Do that until the fifth year.

b) They will pay me a starting salary of $175000 and will increase my salary 25% per year.

The first year is 175000 and 25%, or 1/4, of that is 43750. The salary the second year is 175000+ 43750= 175000+ .25(175000)= 1.25(175000)= $218750. 1/4 of that is 54687.5 so the salary the third year is 218750+ 54687.50= 1.25(218750)= 1.25(1.25(75000))= (1.25^2)(175000). You are correct that it is (175000)(1.25^n).

Contracts on this team are renewed every 5 years.


My question is, which deal should I take and why?


assume that the points can be connected in a continuous line even if the account is only updated yearly, i.e., his salary is only revisited on a yearly basis during this 5 Year period and renegotiated completely after that). Then figure out which deal Lennie should take. Accumulated earnings should be taken into account."

I have no clue how to find the first function. I think it is 200,000^.25x. It might even be 200,000 (1 + .25/1)^1x, right? I am lost.
The second function is, I think, 175,000 x 1.125^x.
I have no idea what to do from here, other than compare the graphs to see which one pays more.

 

[JoshuaTree]

The first year is $200,000, the second year is 200,000+ 40000= $240000, the third year is 240000+ 40000= 200000+ 2(40000)= $280000, etc. Do that until the fifth year.


The first year is 175000 and 25%, or 1/4, of that is 43750. The salary the second year is 175000+ 43750= 175000+ .25(175000)= 1.25(175000)= $218750. 1/4 of that is 54687.5 so the salary the third year is 218750+ 54687.50= 1.25(218750)= 1.25(1.25(75000))= (1.25^2)(175000). You are correct that it is (175000)(1.25^n).

Thank you for confirming my second function. The problem with the first half of your post is that I need a graph. That definitely helps, but without a graph, it shows that I do not understand what I am doing.

 

[JoshuaTree]

You have not answered the question posed in "Read before Posting". Which grade are you in? What type of class is this (Math? Bus? Sports Management?). Please answer these with your reply to following question:

Anyway, the option (a) is growing by a constant amount ($40,000) everyear - the increase is not dependent on the present salary. This is not an exponential function - what type of function is this?

My apologies, I'm new to this forum.
The first function, I assume is linear. The second one, however, is in fact an exponential function. I still need a function for the first one though, even though it is not an exponential function. Wow, I apologize for not thinking of that. You definitely helped bring back the simple functions. I completely forgot about them. It would just be 40000x + 200000

 

[Deleted member 4993]

My apologies, I'm new to this forum.
The first function, I assume is linear.



y = m*x + b

in your case

y = S(x) ← salary after 'x' years

m = 40000

b = 200,000





he second one, however, is in fact an exponential function. I still need a function for the first one though, even though it is not an exponential function.

For plotting use ms-excel.

You still have not answered the question posed in "Read before Posting".

Which grade are you in?

What type of class is this (Math? Bus? Sports Management?).

 

[JoshuaTree]

For plotting use ms-excel.

You still have not answered the question posed in "Read before Posting".

Which grade are you in?

What type of class is this (Math? Bus? Sports Management?).

I did, in fact, answer the questions a little while ago in this thread.
Year 14, Precalc/Calc.

 

[mmm4444bot]

I did, in fact, answer the questions a little while ago in this thread.

Yes, but you edited the information into your original post, well after people had responded in this thread.

Editing your original information after people respond is a bad idea.

Once a response posts in a thread, please post subsequent changes and/or additions in a new post to the thread.

Otherwise, you put volunteers in a position of having to re-read the entire thread while making assumptions regarding what may have changed or what may have been added. Or, people simply miss new information.

That approach often wastes time. Personally, I tend to ignore such threads, once I realize that given information is changing.

Cheers :cool: