Answered

Welcome to Westonci.ca, the place where your questions are answered by a community of knowledgeable contributors. Ask your questions and receive accurate answers from professionals with extensive experience in various fields on our platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

The population of a town in Texas is modeled by the function f(x)=16,007(1.031)x. If the initial population (that is, the population when x=0) was measured January 1, 2014, what will the population be on January 1, 2030? Round your answer to the nearest whole number, if necessary.

The Population Of A Town In Texas Is Modeled By The Function Fx160071031x If The Initial Population That Is The Population When X0 Was Measured January 1 2014 W class=

Sagot :

From the information available, the initial population was 16,007. That figure was taken as at the year zero which is January 1, 2014.

This means

[tex]\begin{gathered} Yr1=2015-2014 \\ Yr2=2016-2014 \\ Yr3=2017-2014 \end{gathered}[/tex]

This trend would be used until we get to January 1, 2030, when we would calculate as follows;

[tex]Yr16=2030-2014[/tex]

Note that the years count from Jan 1 to Jan 1.

The function that models the yearly growth is;

[tex]f(x)=16007(1.031)^x[/tex]

Using the first year, 2014 which is year zero, the result would remain 16,007. That is;

[tex]\begin{gathered} f(0)=16007(1.031)^0 \\ f(0)=16007\times1 \end{gathered}[/tex]

For the 16th year, which is year 2030, we woud now have the following;

[tex]\begin{gathered} f(16)=16007(1.031)^{16} \\ f(16)=16007(1.629816253511204) \\ f(16)=26,088.4687699\ldots \end{gathered}[/tex]

Rounded to the nearest whole number, this figure becomes;

ANSWER:

[tex]\text{Population}\approx26,088[/tex]

Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.