Callie entered an art contest in second grade and won a $1,000 scholarship. The money was invested in an account paying a 9% interest rate compounded annually. The situation can be modeled by the equation a(t)=1,000(1.09)t , where a is the amount in the account after t years. If Callie uses the scholarship 10 years later, determine which graph accurately displays the situation.(1 point)

Answer 1

To determine which graph accurately displays the situation described, we can evaluate the value of the investment after 10 years.

Using the formula provided:

\[ a(t) = 1,000(1.09)^t \]

Substituting \( t = 10 \):

\[ a(10) = 1,000(1.09)^{10} \]

First, we need to calculate \( (1.09)^{10} \).

Calculating \( (1.09)^{10} \):

\[ (1.09)^{10} \approx 2.36736 \]

Now, substituting this value into the equation:

\[ a(10) = 1,000 \times 2.36736 \approx 2367.36 \]

So, after 10 years, the amount in the account would be approximately $2,367.36.

To visualize this situation in graphical format, look for a graph that exhibits exponential growth, starting from $1,000 at \( t = 0 \) and reaching around $2,367 at \( t = 10 \). The curve should rise steeply as time progresses, characteristic of compound interest scenarios.

Find the graph that shows this behavior with these specific values to identify the accurate representation of Callie's investment growth over 10 years.