Question

An exponential function f ( x ) = a ⋅ b x passes through the points (0, 4000) and (3, 2916). What are the values of a and b ?

Answer 1

Answer:

a = 4000, b = 0.9

Step-by-step explanation:

The standard form of an exponential function is

y = a$b^{x}$

To find a and b substitute the given points into the equation

Using (0, 4000), then

4000 = a$b^{0}$ = 4000 × 1 = 4000

Hence a = 4000, thus

y = 4000$b^{x}$

Using (3, 2916), then

2916 = 4000$b^{3}$ (divide both sides by 4000 )

0.729 = $b^{3}$ ( take the cube root of both sides ), thus

b = $\sqrt[3]{0.729}$ = 0.9