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Subject Test Math 2

Question 4 of 28

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SAT Subject Test

Alison deposits $ 500 into a new savings account that earns 5 percent interest compounded annually. If Alison makes no additional deposits or withdrawals, how many years will it take for the amount in the account to double?

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14

Correct Answer: 
No

15

Correct Answer: 
Yes

19

Correct Answer: 
No

20

Correct Answer: 
No

21

Correct Answer: 
No

After 1 year, the amount in the account is equal to $ 500 left parenthesis 1.05 right parenthesis. After 2 years, the amount is equal to $ 500 left parenthesis 1.05 right parenthesis to the power of 2 end exponent, and so on. After n years, the amount is equal to $ 500 left parenthesis 1.05 right parenthesis to the power of n end exponent. You need to find the value of n for which 500 left parenthesis 1.05 right parenthesis to the power of n end exponent invisible times equals 1000. There are several ways to solve this equation. You can use logarithms to solve the equation as follows.

 

 

Since n invisible times equals 14.2, it will take more than 14 years for the amount in the account to double. Thus, you need to round 14.2 up to 15.

Another way to find n is to use your graphing calculator to graph y invisible times equals 500 left parenthesis 1.05 right parenthesis to the power of x end exponent and y invisible times equals 1000. From the answer choices, you know you need to set the viewing window with x values from 0 to about 25 and y values extending just beyond 1000. The x text -coordinate end text of the point of intersection is approximately 14.2. Thus you need to round up to 15.

Question Difficulty: 
medium