MATH SOLVE

4 months ago

Q:
# The number of trucks registered in a city increases by 10% each year. Initially, there were 100 trucks registered. There were 110 trucks registered at the end of Year 1. What is the number of trucks registered in the city at the end of Year 8? Round the answer to the nearest whole number. Enter your answer in the box.

Accepted Solution

A:

Answer:The number of registered trucks is 214.Step-by-step explanation:In order to find the number of trucks, you have to use the Exponential Growth Formula, because the given description represents a quantity (the number of trucks) increasing exponentialy over time with a rate of change proportional to the quantity.The formula is:[tex]Y=a(1+r)^{t}[/tex]Where Y is the amount after time, a is the initial amount, r is the rate of growth and t is the time.In this case:a=100r=10%=10/100=0.1 (Represented as a decimal number)t=8Replacing in the formula:[tex]y=100(1+0.1)^{8}[/tex][tex]y=100(1.1)^{8}=214.35[/tex]Rounding to the nearest whole number:The number of trucks is 214.