precalculus im lost

Question

An exponential function f ( x ) = a ⋅ b x passes through the points (0, 2000) and (2, 980). What are the values of a and b ? a = and b =

Answer 1

f(x) = f(0) = 2000= ab^0 = a

a = 2000

f(2) = 980 = 2000b^2

b^2 = 980/2000 = 98/200 =49/100

b =sqr49/100 = 7/10

f(x) = 2000(7/10)^x = 2000(0.7)^x

Answer 2

This is called "fitting the function f(x) = a.b^x to the two points".

You are given

f(0) = 2000

f(2) = 980

From the first constraint

a.b⁰ = 2000

a.1 = 2000

a = 2000

From the second constraint

a.b² = 980

2000.b² = 980

b² = 980/2000 = 0.49

b = √0.49 = 0.7