In a video game, Jada is building a moon base to support a growing population and to deal with challenges. Jada’s base has a population of 54,500 in the year 2240, and between 2240 and 2270 the population of the base grows exponentially by about 60% per decade.

1. Find the population of Jada’s moon base in 2250 and in 2260 according to this model.
2. The population is a function of the number of decades after 2240. Write an equation for .
3. 1. Explain what means in this situation.
   2. Graph your function using graphing technology, and estimate the value of .
   3. Explain why we can find the value of by multiplying 54,500 by . Find that value.
4. Based on the model, what was the population of Jada’s base in 2258? Show your reasoning.

A chemical is accidentally spilled into a lake and needs to be cleaned up. The cleaning process decreases the amount of the chemical in the lake roughly exponentially. Here is a graph representing , an exponential function that models the amount of chemical left in the lake,  hours after the cleaning begins.

1. Use the graph to estimate , and explain what it tells us in this situation.
2. After one hour, 0.75 liters of the chemical remains in the lake. Find an equation that defines .