Questions: In 2010, the population of the United States was approximately 310 million, with 0.97% annual growth rate. At this rate, the population will be approximately: (a) P(t) = 310(1.0097)^t (b) P(t) = 310 + 0.97t (c) P(t) = 310(1 + 0.0097t) Part of S The function that models the U.S. population (in millions) t years after 2010 is: P(t) = 310(1.0097)^t This indicates that the population is increasing in the exponential fashion. (a) If P(0) = 310, then it represents the population in the year 2010. (b) P(1) = 310(1.0097)^1 = 313.007 million in the year 2011. (c) P(2) = 310(1.0097)^2 = 316.044 million in the year 2012. (d) P(3) = 310(1.0097)^3 = 319.112 million in the year 2013.

In 2010, the population of the United States was approximately 310 million, with 0.97% annual growth rate. At this rate, the population will be approximately:

(a) P(t) = 310(1.0097)^t

(b) P(t) = 310 + 0.97t

(c) P(t) = 310(1 + 0.0097t)

Part of S

The function that models the U.S. population (in millions) t years after 2010 is:

P(t) = 310(1.0097)^t

This indicates that the population is increasing in the exponential fashion.

(a) If P(0) = 310, then it represents the population in the year 2010.

(b) P(1) = 310(1.0097)^1 = 313.007 million in the year 2011.

(c) P(2) = 310(1.0097)^2 = 316.044 million in the year 2012.

(d) P(3) = 310(1.0097)^3 = 319.112 million in the year 2013.

Transcript text: In 2010, the population of the United States was approximately 310 million, with 0.97% annual growth rate. At this rate, the population will be approximately: (a) P(t) = 310(1.0097)^t (b) P(t) = 310 + 0.97t (c) P(t) = 310(1 + 0.0097t) Part of S The function that models the U.S. population (in millions) t years after 2010 is: P(t) = 310(1.0097)^t This indicates that the population is increasing in the exponential fashion. (a) If P(0) = 310, then it represents the population in the year 2010. (b) P(1) = 310(1.0097)^1 = 313.007 million in the year 2011. (c) P(2) = 310(1.0097)^2 = 316.044 million in the year 2012. (d) P(3) = 310(1.0097)^3 = 319.112 million in the year 2013.

Solution

Solution Steps

To solve the problem of determining the population of the United States in future years given an initial population and a constant growth rate, we use an exponential growth model. The formula provided, \( P(t) = 310(1.0097)^t \), represents the population in millions, where \( t \) is the number of years after 2010. We can calculate the population for each year by substituting the respective value of \( t \) into the formula.

Step 1: Initial Population and Growth Rate

The initial population of the United States in 2010 is given as \( P(0) = 310 \) million. The annual growth rate is \( r = 0.0097 \), which leads to a growth factor of \( 1 + r = 1.0097 \).

Step 2: Population Calculation for Each Year

Using the exponential growth model \( P(t) = 310(1.0097)^t \), we can calculate the population for the years 2011, 2012, and 2013.