Problem
5. The population of a small mining town was 13700 in the year 2000 . Each year, the population decreases by an average of $5 \%$. a) What is the exponential equation that models this situation? b) Use your equation to find the population of the town in the year 2010. 6. Five hundred yeast cells in a bowl of warm water doubled in number every $40 \mathrm{~min}$. a) Write an equation that models the number of yeast cells in the bowl, given the number of minutes. b) Use your equation to predict the number of yeast cells in 3 hours. c) Use your equation to predict the number of yeast cells 100 minutes ago.
Solution
Step 1 ：Question 5:
Step 2 ：a) The exponential equation that models this situation is \(y = 13700 * (1 - 0.05)^x\)
Step 3 ：b) The population of the town in the year 2010 is approximately \(\boxed{8203}\)
Step 4 ：Question 6:
Step 5 ：a) The equation that models the number of yeast cells in the bowl, given the number of minutes, is \(y = 500 * (2^{\frac{1}{40}})^x\)
Step 6 ：b) The number of yeast cells in 3 hours is approximately \(\boxed{11314}\)
Step 7 ：c) The number of yeast cells 100 minutes ago is approximately \(\boxed{88}\)
