Question

" According to the U.S. Census Bureau, the population of the United States in 2010 was 308.75 million people. The rate of growth in population was 0.57% per year. Assume that this rate of growth remains the same through 2015. Explain why the population is an exponential function of time.What would you predict the U.S. population to be in 2015? (Round your answer to two decimal places.)"

Answer 1

Answer:

317.65 million

Step-by-step explanation:

We have been given that according to the U.S. Census Bureau, the population of the United States in 2010 was 308.75 million people. The rate of growth in population was 0.57% per year.

Since the population is increasing 0.57% per year, so the rate of change is not linear for the given scenario.

The growth factor (0.57%) remains same, but the population changes each year because it is based on last year's population and not on the original population.

Therefore, the population is an exponential function of time.

We know that an exponential function is in form $y=a\cdot b^x$, where,

y = Final amount,

a = Initial amount,

b = For growth b is in form $(1+r)$, where r represents growth rate in decimal form.

The function for the given scenario would be $P(t)=308.75(1+0.0057)^t$

$P(t)=308.75(1.0057)^t$

To find the approximate U.S. population in 2015, we will substitute $t=2015-2010=5$ in the function.

$P(t)=308.75(1.0057)^5$

$P(t)=308.75*1.0288267572$

$P(t)=317.6502612855$

$P(t)\approx 317.65$

Therefore, the U.S. population would be approximately 317.65 million in 2015.