Word problemIn 1990 the populations of a country was estimated at 4 million. For any year the population is modeled by this logistic equations: p(t)= (240) ÷ (5+54.99e-.0208t) , where is the number of years since 1990. Estimate the year that the population will be 21 million.

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Asked Nov 21, 2019
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Word problem


In 1990 the populations of a country was estimated at 4 million. For any year the population is modeled by this logistic equations: p(t)= (240) ÷ (5+54.99e-.0208t) , where is the number of years since 1990. Estimate the year that the population will be 21 million.

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Expert Answer

Step 1

To estimate the year when the population will be 21 million.

Step 2

Given:

240
p(t)=
5+54.99e.02081
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240 p(t)= 5+54.99e.02081

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Step 3

Substitute 21 for...

240
p (t)=
5 54.99e.020S
240
21=
5 54.99e-0.020 8r
0.020 8
21x (5+54.99e
= 240
1154.79e.020= 240-105
135
e-0.0208
1154.79
Take log on both the sides
135
-0.0208t In
1154.79
1
In
-0.0208 1154.79
135
t =-
t =103.19 years
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240 p (t)= 5 54.99e.020S 240 21= 5 54.99e-0.020 8r 0.020 8 21x (5+54.99e = 240 1154.79e.020= 240-105 135 e-0.0208 1154.79 Take log on both the sides 135 -0.0208t In 1154.79 1 In -0.0208 1154.79 135 t =- t =103.19 years

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Calculus

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