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Sliva [168]
4 years ago
8

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 ?

Mathematics
1 answer:
Alex17521 [72]4 years ago
3 0

Answer:

a = 4000, b = 0.9

Step-by-step explanation:

The standard form of an exponential function is

y = ab^{x}

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

Using (0, 4000), then

4000 = ab^{0} = 4000 × 1 = 4000

Hence a = 4000, thus

y = 4000b^{x}

Using (3, 2916), then

2916 = 4000b^{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

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