(Solved): 1. Find a formula for the function f whose graph is shown in the diagram below. 2. An electricity c ...

1. Find a formula for the function $f$ whose graph is shown in the diagram below. 2. An electricity company charges its customers a base rate of $\$15$ a month plus 8 cents per kilowatt-hour (kWh) for the first 1200 $\mathrm{kWh}$ and 12 cents per $\mathrm{kWh}$ for usage over $1200\mathrm{kWh}$. Write the cost, $C$, in dollars as a function of $x$, the number of $\mathrm{kWh}$ used for $0?x<1500$ and graph the function 3. Suppose that the population of a certain species is given by $P(t)=\frac{1000}{1+9e^{?t}}$ where $t$ is given in years. a. Find the inverse of $P$. b. Use the inverse in a. to find the time required for the population to reach 800 . c. What happens to the population as time goes on, i.e. as $t??$ ?