given P(t)=651,000(0.988)^x, find years for pop. to reach

[Pinku_10]

P(t)=651,000(0.988)^x.

I have to figure out how many years it will take until the population of the town will be 550,000. The problem is, I cannot remember how to solve for x when it's an exponent. I learned how to do it last year in algebra II and I understood it, I just don't remember how to do it now. :?

 

[mmm4444bot]

Re: Precalculus Homework Problem



A = b^x

Solve for x.

x = log[sub:6ap91vsj]b[/sub:6ap91vsj](A)

Don't like base b? Use the Change-of-Base formula.

x = ln(A)/ln(b)

 

[Pinku_10]

Re: Precalculus Homework Problem

The answer in the back of the book says x=13.96, but I can't get that on my calculator with those formulas. I don't know what I'm doing wrong.

 

[stapel]

I don't know what I'm doing wrong.

Until you show your work, I'm afraid we can't know, either. Sorry.

Eliz.

 

[Pinku_10]

Re: Precalculus Homework Problem

I put ln(651000)/ln(0.988). I got a negative number.

 

[Deleted member 4993]

Re: Precalculus Homework Problem

I put ln(651000)/ln(0.988). I got a negative number.

Do the whole problem - with pencil and paper. Where did you use the number 550,000 - the population you want to get to?

Don't just copy some equation and expect correct answer.

 

[mmm4444bot]

Re: Precalculus Homework Problem

I put ln(651000)/ln(0.988). I got a negative number.

Hello Pinku:

Please excuse me if my post confused you. I was not trying to give you a formula to solve your exercise.

I was trying to remind you that when the variable x -- for which you are trying to solve -- is located in the exponent position within some equation, then you need to think: logarithms. We use logarithms to get the variable out of the exponent position.

NOTE: You did not properly type the equation defining the function named P. Function notation says that P(t) is the dependent variable in the functional relationship and t is the independent variable.

Therefore, you must use the symbol t when you write the definition of P. Or, you need to change to P(x).

P(t) = 651,000 * (0.988)^t

Do you know? P(t) is a single number. It's true that four characters comprise this symbol, but alltogether they represent a single variable. The symbol P(t) represents a number, and that number is the population of the town.

P(t) is a variable. It's value varies. It's value depends upon the value of t.

At some time, it's value will be 550000. That's the time which your exercise is asking for. They want to know what value of t is associated with 550000.

You need to write an equation using the definition of P(t) in terms of t which represents the situation where the population is 550000, and then do some algebra to get the equation into the form I showed as a generic example.

A = b^t

Here, A is a single number. You want to get your equation so that there is a single number on the lefthand side.

The symbol b is the base, so the righthand side of your equation should have a power of t.

Please do these first steps, and show us your work. We can go from there.

Cheers,

~ Mark