CPM Homework Help : INT2 Problem 12-109

An exponential function is a function of the form $f\left(x\right) = ab^{x }$ .

What is the equation of an exponential function that passes through the points $\left(1, 6\right)$ and $\left(5, 30.375\right)$ ?

int (a):

Substitute the points to get two equations.

Step (a):

$6 = ab^{1}$
$30.375 = ab^{5}$

Help (a):

Solve for a and b.

Answer (a):

$f\left(x\right) = 4\left(1.5\right)^{x}$

Hint (b):

$\text{How are the graphs of }f(x) = 2^x, f(x) = 3^x, f(x) = \left(\frac{1}{2}\right)^x \text{ different?}$

Hint (c):

Starting value should be $4$ .