Question

An exponential function f(x)=ab^x passes through the points (0,7) and (3, 189). what are the values of a and b?

Answer 1

Answer:

The value of a is 7.

The value of b is 3.

Step-by-step explanation:

We are given the following function:

$f(x) = ab^{x}$

Point (0,7)

This means that when $x = 0, f(x) = 7$. So

$f(x) = ab^{x}$

$7 = ab^{0}$

$a = 7$

So

$f(x) = 7b^{x}$

(3, 189)

This means that when $x = 3, f(x) = 189$. We use this to find b. So

$f(x) = 7b^{x}$

$189 = 7b^{3}$

$b^3 = \frac{189}{7}$

$b^3 = 27$

$b = \sqrt[3]{27}$

$b = 3$

The value of b is 3.