Answer:
To answer this question, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the amount of money after t years
P = the principal (the starting amount of money)
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years
In this problem, we have:
P = $900 (the starting amount)
r = 0.03 (3% as a decimal)
n = 2 (interest is compounded semiannually)
t = time in years
So the formula becomes:
A = $900(1 + 0.03/2)^(2t)
Simplifying:
A = $900(1.015)^2t
We can plot the value of A as a function of t to get the graph that models the worth of the investment over time. The graph would look like an exponential curve, as the value of A grows exponentially over time due to the effect of compound interest.
Here is an example graph that models the worth of the investment over time:
Graph of investment worth over time
The x-axis represents time in years, and the y-axis represents the value of the investment in dollars. The curve shows how the investment grows over time due to the effect of compound interest. As time goes on, the rate of growth increases due to the compounding effect. The graph starts at $900 and grows steadily over time, eventually approaching an asymptotic limit.