Answer:
C. [tex]A(x)=1000\cdot (1+0.17)^x[/tex], where 0.17 is the interest rate.
Step-by-step explanation:
We have been given that a savings account compounds interest, at a rate of 17%, once a year. John puts $1,000 in the account as the principal. We are asked to set up a function to track the amount of money John has.
We will use exponential form of function to set up required function.
An exponential function is in form [tex]y=a\cdot b^x[/tex], where,
a = Initial value,
b = For growth b is in form (1+r), where r represents the growth rate in decimal form.
Let us convert our given rate in decimal form.
[tex]17\%=\frac{17}{100}=0.17[/tex]
Since John invested an amount of $1,000, so a=1000 for our growth function.
Upon substituting our given values in growth function we will get,
[tex]A(x)=1000\cdot (1+0.17)^x[/tex], where A(x) represents amount of money after x years.
Therefore, [tex]A(x)=1000\cdot (1+0.17)^x[/tex] is our required function and option C is the correct choice.
