Question

In 1970 the population of the United States was 203 million. Ten years later, in 1980, the population of the United States was 226 million.
Write a function for the exponential growth of population in the U.S using:

-t(0)=203

-t(0)=226

Answer 1

Answer:

The exponential function for the US population is:

$y = 203\cdot e^{0.0107\cdot t}$

Step-by-step explanation:

Let be supposed that US population can be modelled by means of the following exponential function:

$y = A \cdot e^{B\cdot t}$

Where:

$t$ - Time, measured in years. Where t = 0 for 1970.

$A$ - Initial population, in millions inhabitants.

$B$ - Exponential rate constant, in years.

$y$ - Population, in millions inhabitants.

Each constant is found hereafter:

A

$203 = A \cdot e^{B\cdot 0}$

$203 = A \cdot 1$

$A = 203$

B

$226 = 203\cdot e^{B\cdot 10}$

$\frac{226}{203} = e^{10\cdot B}$

$10\cdot B = \ln \frac{226}{203}$

$B = \frac{1}{10}\cdot \ln \frac{226}{203}$

$B = 0.0107$

The exponential function for the US population is:

$y = 203\cdot e^{0.0107\cdot t}$