Question

PreCalc help?!
Given f(3)=80 and f(6)=120, find f(24) for f(x) as:
a. linear function
b. power function
c. exponential function

Answer 1

Exponential function

Answer 2

a) f(3)=80 -> (x,y)=(3,80)
f(6)=120 -> (x,y) = (6,120)
find slope: (120-80)/(6-3)= 40/3
use y=mx+b to figure out b:
80=(40/3)(3)+b
80=40+b
40=b ....
so f(x)= (40/3)x+40 and f(24)= (40/30)(24)= 360

Answer 3

Thank you for the explaination; I have no idea how to do this stuff. Any idea on how to do the others?

Answer 4

b)\[
f(x)=ax^b\\
80=a(3)^b\\
120=a(6)^b
\]

Answer 5

So what do I do after that? Do I divide by 6 on both sides?

Answer 6

Divide first equation by second equation: \[
\frac 23=\left(\frac 36\right)^b
\]Notice that \(a\)s cancel.

Answer 7

\[
\ln 2/3=b\ln 3/6
\]

Answer 8

Do I put 24 in for b?

Answer 9

No, \[
b=\frac{\ln 2/3}{\ln 1/2}
\]

Answer 10

You can use a calculator to approximate I guess.

Answer 11

Alright, I'll do that. Thanks!

Answer 12

Then use \[
80=a(3)^b
\]To solve for \(a\)