Question

There are 1,000 residents of a town in Year 1. That number increases by 1% each year.

Answer 1

Answer:

Part A) $y=1,000(1.01^{x})$

Part B) $1,105\ persons$

Step-by-step explanation:

Part A) What is the explicit rule for the number of residents

we know that

In this problem we have a exponential function of the form

$y=a(b^{x})$

where

a is the initial value

b is the base

r is the rate

(1+r)=b

so

Let

y ----> the number of residents

x is the time in years

we have

a=1,000 residents

r=1%=0.01

b=(1+0.01)=1.01

substitute

$y=1,000(1.01^{x})$

Part B) How many residents will there be in the town in Year 10?

For x=10 years

substitute in the equation

$y=1,000(1.01^{10})$

$y=1,105\ persons$

Answer 2

Answer:

explicit rule : an =1,000*(1.01)^n-1

amount of the people in the city during the 10th year : 1094