Question

Suppose you start a lawn-mowing business and make a profit of $400 in the first year. Each year, your profit increases 5%. Write a function that models your annual profit. If you continue your business for 10 yr, what will your total profit be?

Answer 1

a). The function is: A=20 t+400, where A=total amount of profit, and t number of years

b). Total profit=$600 after 10 years

Explanation:

a).

The function for the total amount of profits your investment will receive after a given period is given by;

A=P+PRT

where;

A=total amount of profits

P=initial profit

R=rate of increase

T=number of years

In our case;

P=$400

R=5%=5/100=0.05

T=t

replacing;

A=400+(400×0.05×t)

A=400+20 t

A=20 t+400....equation 1

b). Substitute the value of t in equation 1 with 10 years, and solve

A=20 t+400

but;

t=10

replacing;

A=(20×10)+400

A=200+400=600

Total profit=$600 after 10 years