We have been given that you invest $850 into a stock market fund, which grows at a rate of approximately 4% each year. We are asked to write an equation that can be used to calculate the amount of money in the fund after x years.
We will use exponential growth formula to solve our given problem.
An exponential function is in form [tex]y=a\cdot (1+r)^x[/tex], where,
y = Final amount,
a = Initial amount,
r = Growth rate in decimal form,
x = Time.
Let us convert 4% into decimal.
[tex]4\%=\frac{4}{100}=0.04[/tex].
We have [tex]a=840[/tex] and [tex]r=0.04[/tex], so our equation would be:
[tex]y=850\cdot (1+0.04)^x[/tex]
[tex]y=850\cdot (1.04)^x[/tex]
Therefore, the equation [tex]y=850\cdot (1.04)^x[/tex] can be used to calculate the amount of money in the fund after x years.
