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:

`(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`