Question

Using the given table of an exponential function, determine the growth/decay factor as well as the rate of increase/decrease. Type your answers in as numbers. Example: Growth Factor: 3.5, Rate of Increase: 2.5. (Do not input your rate of increase as a percent.)

Answer 1

Growth factor is 1.2

Growth rate is 0.2

Explanation:

Generally, we can have an exponential function as:

y = a(1 + r)^x

Where a is the initial value (y value when x = 0, which is 10)

r is the growth rate

at x = 2

14.4 = 10(1 + r)^2 •••••(i)

at x = 1

12 = 10(1 + r)^1 •••••(ii)

Divide i by ii

14.4/12 = 1 + r

1.2 = 1 + r

r = 1.2-1

r = 0.2

1 + r = 0.2 + 1 = 1.2