%reduction in a decaying exponential function

Question

I am working my way through a calculus book I purchased- Calculus- Single and Multivariable (3rd edition) by Hughes-Hallet et al.

I am having issues with the following question

"When the olympic games were held outside Mexico City in 1968, there was much discussion about the effect the high altitude (7340 feet) would have on the athletes. Assuming air pressure decays exponentially by 0.4% every 100 feet, by what percentage is air pressure reduced by moving from sea level to Mexico City?"

My answer

$$100-(100\cdot 0.996^{734})= 94.72\%$$

The textbook gives the correct answer as $25.5\%$.

Can somebody explain where I might have gone wrong.

Answer 1

You did the division wrong. 7340 feet is 73.4 times 100 feet, not 734 times 100 feet.

So you indeed get, at 7340 feet, a reduction of the pressure to $0.996^{73.4} \approx 0.745$ of it's original value. Which amounts to a reduction of $\approx 25.5\%$.

I found your mistake, BTW, by solving $$ 0.996^x = 0.745 \Rightarrow x = \log_{0.996} 0.745 = \frac{\ln 0.745}{\ln 0.996} \approx 73.4 \text{.} $$