SOLUTION: The growth of a certain species​ (in millions) since 1970 closely fits the following exponential function where t is the number of years since 1970. A(t)=3500e^0.0166t a. T

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: The growth of a certain species​ (in millions) since 1970 closely fits the following exponential function where t is the number of years since 1970. A(t)=3500e^0.0166t a. T      Log On


   

Question 1122142: The growth of a certain species​ (in millions) since 1970 closely fits the following exponential function where t is the number of years since 1970.
A(t)=3500e^0.0166t
a. The population of the species was about 4142 million in 1980. How closely does the function approximate this​ value?
b. Use the function to approximate the population of the species in 2000.​ (The actual population in 2000 was about 5869 ​million)
c. Estimate the population of the species in the year 2015.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Not as A(t)=3500e^0.0166t

but as A(t)=3500e^(0.0166t).


A%28t%29=3500e%5E%280.0166t%29

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a. The population of the species was about 4142 million in 1980. How closely does the function approximate this​ value?
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That is t=10.
A%2810%29=3500e%5E%280.0166%2A10%29
A=3500e%5E%280.166%29
A=4132
This is a difference of 10 million.
The model is a bit low by 0.24%.


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b. Use the function to approximate the population of the species in 2000.​ (The actual population in 2000 was about 5869 ​million)
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That is 30 years past 1970.
Use t=30. Evaluate A.