A function h(t) is known to be exponential; that is h(t)=ab^t. if h(3)=6 and h(5)=24 find b and a

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asked Mar 18, 2023 43.2k views

1 Answer

Primulaveris · Answer 1 · 2023-03-23T02:09:40+0000

We have:

6 = ab^3

24 = ab^5

If you divide the second equation by the first:

(24)/(6) = (ab^5)/(ab^3)

4 = b^2

b = 2 (we discard the negative solution because in the exponential function the base must be positive.)

Then:

$6 = a\cdot 2^3$

$6 = a\cdot 8$

a = (6)/(8)

a = (3)/(4) = 0.75