Use the exponential growth model, A=A_0e^{kt}. In 1975, the population of Europe was 679 million. By 2015, the population had grown to 746 million. So

avissidep

avissidep

Answered question

2021-02-21

Use the exponential growth model, A=A0ekt. In 1975, the population of Europe was 679 million. By 2015, the population had grown to 746 million.
Solve,
a. Find an exponential growth function that models the data for 1975 through 2015.
b. By which year, to the nearest year, will the European population reach 800 million?

Answer & Explanation

Daphne Broadhurst

Daphne Broadhurst

Skilled2021-02-22Added 109 answers

Find an exponential growth function that modeled the data from 1975 to 2015.
In 1975, the population of Europe estimated as 679 million and in 2015, the population had grown to 746 million.
The exponential frowth model can be expressed as A=A0ekt
Consider the initial year 1975 as t=0 such that A0=679
And t=40 for 2015 such that A(40)=746.
Substitute the t=40, A0=679 in A=A0ekt
A(40)=679ek(40)
746=679e40k
e40k=746679
k=140ln(746679)
k0.00235
Hence the exponential growth function such that the data for 1975 through 2015 is A=679e0.00235t
(b) Find the year in which the European population will reach 800 million.
From part (a), the exponential growth function such that the data for 1975 through 2015 is A=679e0.00235t
In order to find the year such that the population will reach 800 million, substitute 800 for A in A=679e0.00235t
800=679e0.00235t
e0.00235t=800679
0.00235t=ln(800679)
t=ln(800679)0.00235
t70
The year becomes 1975+70=2045
Hence, the year in which the European population will reach 800 million is 2045.

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