Question

exponential models guided practice example suppose the rate of increase for the u.s. population is 1.4% instead of 1.24%. assume the starting population is still 281 million. type your answer and then click or tap done. use the ^ symbol (shift+6 on the keyboard) to signify an exponent. for example, for 2 to the third power, enter 2^3. write the exponential function that incorporates this new rate of increase. p(x)= rate increase exponential growth function p(x) = e(1.0124)^x ? growth factor(b) 1.0124 1.014 rate of increase 1.24% 1.4%

Explanation:

Step1: Recall exponential growth formula

The general form of an exponential growth function is $p(x) = a(1 + r)^x$, where $a$ is the initial amount, $r$ is the rate of increase (in decimal), and $x$ is the time variable.

Step2: Identify values of $a$ and $r$

• The initial population $a$ is 281 million (given: "the starting population is still 281 million").
• The new rate of increase is 1.4%. To convert this percentage to a decimal, we divide by 100: $r=\frac{1.4}{100}=0.014$.
• Then, $1 + r = 1+0.014 = 1.014$.

Step3: Substitute values into the formula

Substitute $a = 281$ and $1 + r = 1.014$ into the exponential growth formula $p(x)=a(1 + r)^x$. We get $p(x)=281(1.014)^x$.

Answer:

$p(x) = 281(1.014)^x$