Question

Find C and a so that f(x)=CA^x f(0)=3 and f(2)=12

Answer 1

The function is:

`f(x)=3 \cdot 2^x`

`C=3`

`A=2`

Explanation:

`f(x)=C\cdot A^x`

Let's plug in the first point (0,3):

`f(0)=C \cdot A^0`

`3=C\cdot 1`

`3=C`

So we have:

`f(x)=3 \cdot A^x`

Let's use the other point (2,12):

`f(2)=3 \cdot A^2`

`12=3 \cdot A^2`

Divide both sides by 3:

`(12)/(3)=A^2`

`4=A^2`

Square root both sides:

`\pm √(4)=A`

`\pm 2=A`

Exponential functions have positive bases so
`A=2`.

The function is:

`f(x)=3 \cdot 2^x`

`C=3`

`A=2`