**A total of two questions refer to the following information.Jessica opened a ban...**

### Question

**A total of two questions 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.

(1 of 1) What is the value of *x *in the expression?

*This is a short or long answer (free choice) question. The student will not be provided with options and will be required to enter their answer in a provided field.*

Any of the following can be considered correct answers to the question: 1.02.

### Explanation:

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.

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