Part A

Question

Select the equation which represents the given scenario.

Charlotte purchased a rare coin from a dealer for $200. The value of the coin increases 7% each year.

t= number of years

y= value of coin

(1 point)
Responses

200+0.7t=y
200 plus 0 point 7 t is equal to y

200(1.07)t=y
200 times 1 point 0 7 to the t th power is equal to y

200(0.07)1=y
200 times 0 point 0 7 to the 1th power is equal to y

1.07t2+200t=y
1 point 0 7 t squared plus 200 t is equal to y
Question 2
Part B

Using the scenario from Part A, what is the value of the coin in 6 years?

Be sure to round your answer to the nearest cent.

(1 point)
Value of the coin in 6 years=

Answer 1

Part A

The correct equation that represents the scenario is:

200(1.07)^t = y

This equation indicates that the initial value of the coin is $200, and it increases by 7% every year, represented by multiplying by 1.07 raised to the power of t (the number of years).

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Part B

To find the value of the coin in 6 years, we can substitute t = 6 into the equation:

\[ y = 200(1.07)^t \]

Calculating for t = 6:

\[ y = 200(1.07)^6 \]

First, calculate \( (1.07)^6 \):

\[ (1.07)^6 \approx 1.484812 \]

Now, multiply by 200:

\[ y \approx 200 \times 1.484812 \approx 296.9624 \]

Rounding to the nearest cent, the value of the coin in 6 years is:

$296.96