Question

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

Answer 1

Answer:

The function is:

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

$C=3$

$A=2$

Step-by-step 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:

$\frac{12}{3}=A^2$

$4=A^2$

Square root both sides:

$\pm \sqrt{4}=A$

$\pm 2=A$

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

The function is:

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

$C=3$

$A=2$