How do you find formulas for the exponential functions satisfying the given conditions h(0)=3 and h(1)= 15?

1 Answer
Oct 25, 2016

An exponential function is a function of the form #y = ab^x#.

Knowing the inputs and outputs of the function, we can write a systems of equations, with respect to #a# and #b# to represent the problem.

#3 = ab^0#
#15 = ab^1#

The simplest way of solving this system will be using the fact that #n^0, n in RR = 1#. So, we immediately know that #a = 3#.

We insert #a = 3# into the second equation to get #b = 5#.

So, the exponential function is #y = 3(5)^x#.

Hopefully this helps!