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)f(x)=35x

Explanation:

We have:

Ca^0=3Ca0=3

Ca^1=15Ca1=15

Ca^0=3=>C=3Ca0=3C=3

So:

3a=15=>a=53a=15a=5

This gives:

f(x)=3*5^xf(x)=35x

Jul 22, 2018

f(x)=3(5)^xf(x)=3(5)x

Explanation:

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

Ca^0=3rArrC=3Ca0=3C=3

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

3a^1=15rArra=15/3=53a1=15a=153=5

f(x)=3(5)^xf(x)=3(5)x

Jul 22, 2018

f(x)=3*5^xf(x)=35x.

Explanation:

Let, f(x)=ca^xf(x)=cax.

"Given that "f(0)=3 rArr ca^0=3 rArr c=3Given that f(0)=3ca0=3c=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.