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

What is the explicit rule for the number of residents and how many residents will there be in the town in Year 10?


Round to the nearest person.

Drag and drop the answers into the boxes to match the situation.
Explicit rule
Amount of people in the city during the 10th year.

Respuesta :

calculista

Answer:

Part A) [tex]y=1,000(1.01^{x})[/tex]

Part B) [tex]1,105\ persons[/tex]

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

[tex]y=a(b^{x})[/tex]

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

[tex]y=1,000(1.01^{x})[/tex]

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

For x=10 years

substitute in the equation

[tex]y=1,000(1.01^{10})[/tex]

[tex]y=1,105\ persons[/tex]

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