Question

An exponential function f(x)= ab^x passes through the points (0,10) and (3,1250). What are the values of a and b?

a = I know it’s 10
b = ?

Answer 1

a = 10 and the next would probably be b=5

Answer 2

a = 10 and b = 5

Explanation:

We write out f(x)= ab^x for x = 0 and x = 3 to create two equations in a and b that must be solved simultaneously:

(0, 10): 10 = a*b^0

This tells us that 10 = a*1, or a = 10.

(3, 1250): 1250 = a*b^3 => 10*b^3, or

1250 = 10*b^3, or

125 = b^3. Taking the cube root of both sides, we obtain b = 5.

a = 10 and b = 5