We have been given that sales of cases of bottled water are up 7% from last year. You sold 900 cases of bottled water last year. We are asked to find the the forecast before total sales of cases of bottled water in three years.
We will use exponential growth function to solve our given problem.
An exponential growth function is in form [tex]y=a\cdot (1+r)^x[/tex], where
y = Final value,
a = Initial value,
r = Growth rate in decimal form,
x = Time.
[tex]7\%=\frac{7}{100}=0.07[/tex]
[tex]y=900\cdot (1+0.07)^x[/tex]
[tex]y=900\cdot (1.07)^x[/tex]
Let us find bottles sold last year by substituting [tex]x=1[/tex] in our formula as:
[tex]y=900\cdot (1.07)^1[/tex]
[tex]y=963[/tex]
Now our initial value would be 963.
Now we will substitute [tex]x=3[/tex] to solve our given problem.
[tex]y=963\cdot (1.07)^3[/tex]
[tex]y=963\cdot 1.225043[/tex]
[tex]y=1179.716409[/tex]
Upon rounding to nearest whole number, we will get:
[tex]y\approx 1180[/tex]
Therefore, the total sales of cases of bottled water in 3 years would be 1180 and option A is the correct choice.
