How do you find formula for the exponential function in the form of f(x)= Ca^x given f(0)=3 and f(1)=15?

3 Answers
Jul 22, 2018

color(blue)(f(x)=3*5^x)

Explanation:

We have:

Ca^0=3

Ca^1=15

Ca^0=3=>C=3

So:

3a=15=>a=5

This gives:

f(x)=3*5^x

Jul 22, 2018

f(x)=3(5)^x

Explanation:

"substitute "(0,3)" into the equation"

Ca^0=3rArrC=3

"substitute "(1,15)" into the equation"

3a^1=15rArra=15/3=5

f(x)=3(5)^x

Jul 22, 2018

f(x)=3*5^x.

Explanation:

Let, f(x)=ca^x.

"Given that "f(0)=3 rArr ca^0=3 rArr c=3.

:. f(x)=ca^x=3a^x.

"Also "f(1)=15 rArr 3a^1=15 rArr a=5.

"Thus, "f(x)=ca^x, c=3, a=5.

rArr f(x)=3*5^x.