6.7 problem 7 Suppose P=f(t) is the population (in thousands) of town t years after 1990, and that f(7)=15 and f(12)=25,

(a) Find a formula for f(t) assuming f is exponential in the form ab^t. Use 5 decimal places for a & b: P=f(t)=

(b) Find a formula for f−1(P)=

(c) Evaluate f(45)=

(d) f−1(45)=

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:

The town's population in 2045 is f(45) people.
The town's population has grown by f(45) people over a 45 year period.
The town's population in 2035 is f(45) people.
The town's population will reach 45,000 people in f−1(45) years after 1990.
The town's population will reach 45,000 people in f−1(45) years from now.
The town's population will reach 45 people in f−1(45) years after 1990.
The town's population in 2035 is f(45) thousand people.

(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).