1question i need help on please :)ASAP

[susu]

Hey, can someone help me with this one question i don't understand and explain it thoroughly. I've been trying to solve it but i'm not getting it. Thank you to whomever does solve it. I appreciate it.


The question states. "Find the function of the form f(x) = Ca^x whose graph is given with the point (2,80)"

-Thanks again

 

[susu]

Nope. IT doesn't say anything else. it shows a graph but it's just an increasing exponential graph with the point (2,80)

 

[susu]

here's the picture

 

[susu]

f(2)=80 and F(5)=0?

 

[susu]

i mean f(0)=5

 

[susu]

Right

\(\displaystyle f(2) = 80,\ and\ f(0) = 5. \)

Excellent. You get that from the graph. But you are also given f(x) in formula terms, C, a, and x.

In those terms what is f(2)?

What is f(0)?

I mean f(2)=Ca^2 and f(0)=Ca^0 ? but what's throwing me off is that there's two constants. but i know anything raised to the power 0 would =1 so would that cancel out the a?

 

[susu]

Whoa slow down.

\(\displaystyle 80 = f(2) = Ca^2.\)

\(\displaystyle 5 = f(0) = Ca^0.\)

Two unknowns, C and a, but two equations. That means that if the equations are consistent and independent, there are a finite number of solutions, right? Now this is NOT a system of linear equations, but I can see at least three ways to solve the system. You have already identified one.

\(\displaystyle 5 = Ca^0 = ?????\)

So C=5?

 

[susu]

BINGO You have it

\(\displaystyle 5 = Ca^0 = C * 1 = C.\)

Now substitute C into your other equation: \(\displaystyle 80 = Ca^2.\)

You are almost at the end of the road EXCEPT you must determine whether both solutions of your equation are acceptable answers.

Okay, so a^2=16 so a=4

 

[susu]

There you go. The right answer is indeed a = 4. Now for extra credit, why CAN'T the answer be a = - 4?

because in an exponential equation doesn't it have to be greater than 0

 

[susu]

Thank you very much! I understand the concept now. Appreciate it.

 

[Deleted member 4993]

I mean f(2)=Ca^2 and f(0)=Ca^0 ? but what's throwing me off is that there's two constants. but i know anything raised to the power 0 would =1 so would that cancel out the a?

Correct → C = 5

Now use the point (2,80) to find 'a'.