Question

Identify the initial value, a, and base, b, of the function f(x)=ab^x if its graph passes through the points (0, 4) and (1, 20)

Answer 1

a = 4, b = 5

Explanation:

Given the exponential function

f(x) = a
`b^(x)`

Use the given points to find a and b

Using (0, 4 ) , then

4 = a
`b^(0)` (
`b^(0)` = 1 ) , thus

a = 4 , so

f(x) = 4
`b^(x)`

Using (1, 20 ) , then

20 = 4b ( divide both sides by 4 )

b = 5