Question

Suppose the population of a town was 40,000 on January 1, 2010
and was 50,000 on January 1, 2015.

Let P(*t*) be the population of the town in thousands of
people *t* years after January 1, 2010.

(a) Build an exponential model (in the form P(t) =
*a**b^{t} ) that relates P(t) and t. Round the value
of b to 5 significant figures.

(b) Write the exponential model in the form P(t) =
a*e^{kt}. According to this model, what is the growth rate
of the population? Your answer should be accurate to
four significant figures, and expressed as a percentage. This means
that if you obtain k=0.045678, you should type 4.568%

(c) Use the model to estimate the town's population (to the nearest integer) on January 1, 2040.

(d) Estimate the year when the town's population first exceeds 120,000.

Answer #1

Suppose the population of a town was 40,000 on January 1, 2010
and was 50,000 on January 1, 2015. Let P(t) be the
population of the town in thousands of people t years
after January 1, 2010.
Build an exponential model (in the form P(t) = a
bt ) that relates P(t) and t. Round the value of b to 5
significant figures.
a = ?
b = ?

(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
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