refer to the following information.
Jessica opened a bank account that earns 2 percent interest compounded annually. Her initial deposit was $100, and she uses the expression $100(x)^{t} to find the value of the account after t years.
Jessica’s friend Tyshaun found an account that earns 2.5 percent interest compounded annually. Tyshaun made an initial deposit of $100 into this account at the same time Jessica made a deposit of $100 into her account. After 10 years, how much more money will Tyshaun’s initial deposit have earned than Jessica’s initial deposit? (Round your answer to the nearest cent and ignore the dollar sign when gridding your response.)

Solution
The correct answer is 6.11. Jessica made an initial deposit of $100 into her account. The interest on her account is 2 percent compounded annually, so after 10 years, the value of her initial deposit has been multiplied 10 times by the factor 1 + 0.02 = 1.02. Hence, after 10 years, Jessica’s deposit is worth $100(1.02)^{10} = $121.899 to the nearest tenth of a cent. Tyshaun made an initial deposit of $100 into his account. The interest on his account is 2.5 percent compounded annually, so after 10 years, the value of his initial deposit has been multiplied 10 times by the factor 1 + 0.025 = 1.025. Hence, after 10 years, Tyshaun’s deposit is worth $100(1.025)^{10} = $128.008 to the nearest tenth of a cent. Hence, Jessica’s initial deposit earned $21.899 and Tyshaun’s initial deposit earned $28.008. Therefore, to the nearest cent, Tyshaun’s initial deposit earned $6.11 more than Jessica’s initial deposit.
refer to the following information.
Jessica opened a bank account that earns 2 percent interest compounded annually. Her initial deposit was $100, and she uses the expression $100(x)^{t} to find the value of the account after t years.
What is the value of x in the expression?

Solution
The correct answer is 1.02. The initial deposit earns 2 percent interest compounded annually. Thus at the end of 1 year, the new value of the account is the initial deposit of $100 plus 2 percent of the initial deposit: $100 + \(\frac{2}{100}\) ($100) = $100(1.02). Since the interest is compounded annually, the value at the end of each succeeding year is the sum of the previous year’s value plus 2 percent of the previous year’s value. This is again equivalent to multiplying the previous year’s value by 1.02. Thus, after 2 years, the value will be $100(1.02)(1.02) = $100(1.02)^{2} ; after 3 years, the value will be $100(1.02)^{3}; and after t years, the value will be $100(1.02)^{t} . Therefore, in the formula for the value for Jessica’s account after t years, $100(x)^{t} , the value of x must be 1.02.
h(x)=\(\frac{1}{(x − 5)^{2} + 4(x − 5) + 4}\)
For what value of x is the function h above undefined?

Solution
The correct answer is 3. The function h(x) is undefined when the denominator of \(\frac{1}{(x − 5)^{2} + 4(x − 5) + 4}\) is equal to zero. The expression (x − 5)^{2} + 4(x − 5) + 4 is a perfect square: (x − 5)^{2} + 4(x − 5) + 4 = ((x − 5) + 2)^{2}, which can be rewritten as (x − 3)^{2}. The expression (x − 3)^{2} is equal to zero if and only if x = 3. Therefore, the value of x for which h(x) is undefined is 3.