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(1 point) Suppose P=f(t)P=f(t) is the population (in thousands) of town tt years after 1990, and...

(1 point) Suppose P=f(t)P=f(t) is the population (in thousands) of town tt years after 1990, and that f(4)=14f(4)=14 and f(12)=21f(12)=21,

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

(b) Find a formula for f−1(P)=f−1(P)=

(c) Evaluate f(30)=f(30)=  (Round your answer to the nearest whole number.)

(d) f−1(30)=f−1(30)=  (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 2020 is f(30)f(30) people.
  2. The town's population will reach 30,000 people in f−1(30)f−1(30) years from now.
  3. The town's population will reach 30 people in f−1(30)f−1(30) years after 1990.
  4. The town's population has grown by f(30)f(30) people over a 30 year period.
  5. The town's population will reach 30,000 people in f−1(30)f−1(30) years after 1990.
  6. The town's population in 2020 is f(30)f(30) thousand people.
  7. The town's population in 2030 is f(30)f(30) 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).

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Hope explanation is clear.

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