Question

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the population of india in 2013 was about 1.26 billion. assume that the population of india continues to grow exponentially at the growth rate of 0.75% per year. thus, the expected population of india, in billions of people, t years after 2013, is given by the function ( p(t) = 1.26e^{0.0075t} ). determine the expected population of india in 2018
the expected population is ( square ) billion people
(simplify your answer. round to the nearest hundredth as needed)

Explanation:

Step1: Calculate the value of \(t\)

The year 2018 is \(2018 - 2013=5\) years after 2013. So \(t = 5\).

Step2: Substitute \(t = 5\) into the population function

We have \(P(t)=1.26e^{0.0075t}\). Substitute \(t = 5\) into it: \(P(5)=1.26e^{0.0075\times5}\).
First, calculate \(0.0075\times5 = 0.0375\). Then \(P(5)=1.26e^{0.0375}\).
Since \(e^{0.0375}\approx1.0382\) (using a calculator for the exponential function \(y = e^{x}\), where \(x = 0.0375\)).
Then \(P(5)=1.26\times1.0382\).

Step3: Calculate the final result

\(1.26\times1.0382=1.31\) (rounded to the nearest hundredth).

Answer:

\(1.31\)