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In 2012, the population of a city was 6.29 million. The exponential growth rate was
2.41% per year.
a) Find the exponential growth function.
b) Estimate the population of the city in 2018.
c) When will the population of the city be 8 million?
d) Find the doubling time.
a) The exponential growth function is P(t) = 6.29 e 0.02411, where t is in terms of
the number of years since 2012 and P(t) is the population in millions.
(Type exponential notation with positive exponents. Do not simplify. Use integers
or decimals for any numbers in the equation.)
b) The population of the city in 2018 is million.
(Round to one decimal place as needed.)
c) The population of the city will be 8 million in about years after 2012.
(Round to one decimal place as needed.)
d) The doubling time is about years.
(Simplify your answer. Round to one decimal place as needed.)

Sagot :

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Answer:

  a) P(t) = 6.29e^(0.0241t)

  b) P(6) ≈ 7.3 million

  c) 10 years

  d) 28.8 years

Step-by-step explanation:

a) You have written the equation.

  P(t) = 6.29·e^(0.0241·t)

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b) 2018 is 6 years after 2012.

  P(6) = 6.29·e^(0.0241·6) ≈ 7.2686 ≈ 7.3 . . . million

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c) We want t for ...

  8 = 6.29·e^(0.0241t)

  ln(8/6.29) = 0.0241t

  t = ln(8/6.29)/0.0241 ≈ 9.978 ≈ 10.0 . . . years

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d) Along the same lines as the calculation in part (c), doubling time is ...

  t = ln(2)/0.0241 ≈ 28.7613 ≈ 28.8 . . . years

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