Suppose $P=f(t)$ is the population (in thousands) of town $t$ years after 1990, and that $f(3)=11$ and $f(9)=20$,

(a) Find a formula for $f(t)$ assuming $f$ is exponential: $P = f(t) =$

(b) Find a formula for $f^{-1}(P) =$

(c) Evaluate $f(50) =$ (Round your answer to the nearest whole number.)

(d) $f^{-1}(50) =$ (Round your answer to at least one decimal place.)

Write out sentences to explain the practical meaning of your answers to parts (c) and (d). Consider the seven numbered statements in the list below:

1. The town's population in 2040 is $f(50)$ people.
2. The town's population will reach 50,000 people in $f^{-1}(50)$ years after 1990.
3. The town's population will reach 50 people in $f^{-1}(50)$ years after 1990.
4. The town's population in 2050 is $f(50)$ people.
5. The town's population has grown by $f(50)$ people over a 50 year period.
6. The town's population in 2040 is $f(50)$ thousand people.
7. The town's population will reach 50,000 people in $f^{-1}(50)$ years from now.

(e) Which statement above explains the meaning of your answer to (c)? (enter the number 1-7 of the correct statement).

(f) Which statement above explains the meaning of your answer to (d)? (enter the number 1-7 of the correct statement).