Question

name: harris, lashea j.
per.
date: cw6
132 pts

1. the first year of a charity walk event had an attendance of 500. the attendance y increases by 5% each year.

a. write an exponential growth function to represent this situation.
b. how many people will attend in the 10th year? round your answer to the nearest person.

1. the population of a small town was 3600 in 2005. the population increases by 4% annually.

a. write an exponential growth function to represent this situation.
b. what will the population be in 2025? round your answer to the nearest person

Explanation:

Problem 9

Step1: Define exponential growth formula

The standard exponential growth formula is $Y = a(1+r)^x$, where $a$ = initial amount, $r$ = annual growth rate, $x$ = time in years.

Step2: Write the function for Q9A

Here, $a=500$, $r=0.05$. Substitute values:
$Y = 500(1+0.05)^x$

Step3: Calculate time for Q9B

For the 10th year, $x=10$. Substitute into the function:
$Y = 500(1.05)^{10}$
First compute $(1.05)^{10} \approx 1.62889$
Then calculate $Y = 500 \times 1.62889 \approx 814.445$
Round to nearest person.

Step1: Define exponential growth formula

Use $Y = a(1+r)^x$, where $a$ = initial population, $r$ = annual growth rate, $x$ = time in years.

Step2: Write the function for Q10A

Here, $a=3600$, $r=0.04$. Substitute values:
$Y = 3600(1+0.04)^x$

Step3: Calculate time for Q10B

Time from 2005 to 2025: $x=2025-2005=20$. Substitute into the function:
$Y = 3600(1.04)^{20}$
First compute $(1.04)^{20} \approx 2.19112$
Then calculate $Y = 3600 \times 2.19112 \approx 7888.03$
Round to nearest person.

Answer:

A. $Y = 500(1.05)^x$
B. 814

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Problem 10