Give the growth factor that corresponds to 282% growth.

Answer 1

282% growth, if annual growth, means after one year 100 grows to 382, since 282 growth = 282 + origninal amount sums to 382

if the growth rate is continuous, compounded continuously, which is natural, in nature, such as the growth of trees or plants, or similar continuous decay (negative growth) rates, then

382= 100e^rt where t = number of years and r = the growth rate

3.82 = e^rt

take natural logs of both sides

ln3.82 = rt

r = (ln3.82)/t which for one year with t=1, = ln3.82 = about 1.34 = 134% annual rate of growth

start with 100 at t =0

at t=1, 100 grows to 382

t =2 382 grows to 3.82(382) = about 1459

A = Pe^1.34t is the applicable natural exponential function

A = 100e^1.34(2) = 100(e^2.68) = 100(14.59) = 1,459

r= annual growth rate = 134% = 1.34