Question

An automobile engine loses approximately 3% of its power for every thousand feet of elevation gain. A certain engine generates 180 horsepower at sea level. How much will it generate at an elevation of 4000 feet? Round to the nearest whole number

Answer 1

I think We could learn something if we knew what the factor t/c was

Answer 2

`\bf \textit{Periodic/Cyclical Exponential Decay} \\\\ A=P(1 - r)^{(t)/(c)}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\to &180\\ r=rate\to 3\%\to (3)/(100)\to &0.03\\ t=\textit{elevation feet}\to &4000\\ c=period\to &1000 \end{cases} \\\\\\ A=180(1-0.03)^{(4000)/(1000)}\implies A=180(0.97)^4\implies A= 159.3527058`

periodic or cyclical, because every 1000 feet, is losing 3% of the remaining horsepower, so the every cycle of 1000 feet, 3% is getting hosed.