Question

An exponential function f(x)=ab^x passes through points (0,5000) and (3,2560). What are values of a and b?

Answer 1

a = 5000

b = 0.8

Explanation:

f(x) = abˣ

Plugging in the points:

5000 = ab⁰

2560 = ab³

b⁰ is 1, so the first equation reduces to:

5000 = a

Plugging into the second equation:

2560 = 5000b³

0.512 = b³

b = 0.8

Therefore, a = 5000 and b = 0.8.