Question

Identify the amount (a) and the growth factor (b) in each exponential function. Break B into (1+r) where the rate of growth. Give r as a percentage.

y=1.07 (1.96)x
a
b=
r(as a percentage)

Answer 1

a = 1.07

b = 1.96

r = 96%

Explanation:

In an exponential function, modeled by f(x) = a(b)ˣ, a is the initial value and b is the growth factor. If we apply this formula to the given function y = 1.07(1.96)ˣ, we can see that the initial value, a, is 1.07, and the growth factor, b, is 1.96.

Now, to break down b, 1.96, into a rate, you simply set it equal to the problem’s given (1 + r) equation to find the rate.

1.96 = 1 + r

So r = .96

Now, we just have to convert .96 into a percentage to get a growth rate of 96%.