I do not want the answer given to me, I just want assistance.
Problem: Marcus invests $750 in an account that pays 9.8% interest compounded annually. Write a function that describes the account balance, A, in terms of the number of years, t, that have passed.
I know that to find the account balance after one year:
A + (A * 0.098) A + 0.098A (simplified)
But I don't know how to implement the time variable.
initial balance is $750 after one year 750 + (750*0.098) = 1348.5
after 2 years: 1348.5 + (1348.5*0.098) = 1480.653
Hint: Your formula is not quite right.
The initial balance (at time $t=0$) is $$A(0)=\boxed{750}$$
After one year (at time $t=1$), the balance is $$A(1) = 750 + (0.098)\cdot 750 = \boxed{750 \cdot(1.098)}$$
Let's leave it "unmultiplied" so you can see the pattern as it develops.
The entire amount now remains to accrue additional interest, so $A(1)$ is the principal for the upcoming second year.
After two years (at time $t=2$), the balance is $$A(2) = A(1) + (0.098)\cdot A(1) =\underbrace{A(1)}_{750\cdot(1.098)}\cdot(1.098)=\boxed{750(1.098)^2}$$
Again the entire amount remains to accrue additional interest. Do you see the pattern here? Can you say what happens for the third year, the fourth year etc.? So finally, what do you think $A(t)$ is, the balance after $t$ years?