The hourly wage of of workers was raised once a year and grew exponentially from $ 9.00 to $ 13.81 in 8 years.

Question

The hourly wage of workers was raised once a year and grew exponentially from $9.00 to $13.81 in 8 years. What was the growth rate?

The growth rate was %.  Round nearest 0.1%

Answer 1

This exponential growth problem gives you the beginning (No) and ending (N(t)) values, and the time "t" it took to get there, but compounding is yearly not continually, so we do not use the exponential function. Thus we have N(t) = No * (1+ g)^t, or in this case, 13.81 = 9.00 * (1 + g)⁸

Solve for "g" by doing the algebra on this equation.

Note this is similar to money in savings growing at a rate of "g*100" percent per year, calculated on a yearly basis.

Answer 2

This is exponential annual growth.

13.81 = 9(x⁸) where x is 1 + the growth rate expressed as a decimal.

13.81/9 = x⁸

1.5344 = x⁸

Take logs of both sides: log1.5344 = 8logx

0.18594/8 = logx

0.02324 = logx

x = 1.05497 so the growth rate is 5.497%/yr or 5.5%/yr to the nearest tenth of a pct.

Answer 3

13.81 = 9e^8r_; r = ln(13.81/9)/8 = 0.0535 = 5.4%