Question

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

Answer 1

We have:

$6 = ab^3$

$24 = ab^5$

If you divide the second equation by the first:

$\dfrac{24}{6} = \dfrac{ab^5}{ab^3}$

$4 = b^2$

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

Then:

$6 = a\cdot 2^3$

$6 = a\cdot 8$

$a = \dfrac{6}{8}$

$a = \dfrac{3}{4} = 0.75$