QuestionInterpret the expression $10,785(1.0275)^{x}$ : What are the initial investment and growth rate? Choose A, B, C, D, or E.

Studdy Solution

STEP 1

Assumptions1. The expression $10,785(1.0275)^{x}$ represents the amount of money in an investment account with interest that compounds. . The number $10,785$ represents the initial investment amount.
3. The number $1.0275$ represents the growth rate of the investment.
4. The variable $x$ represents the number of compounding periods.

STEP 2

The initial investment is the coefficient of the exponential function, which is $10,785.$ $Initial\,investment = \$10,785$ $

STEP 3

The growth rate of the investment is the base of the exponent, subtracted by1 and expressed as a percentage. $Growth\,rate = (1.0275 -1) \times100\%$

STEP 4

Calculate the growth rate.
$Growth\,rate = (1.027 -1) \times100\% =2.75\%$ The initial investment is $\$10,785$ and the growth rate of the investment is $2.75\%$ . Therefore, the correct answer is. The initial investment is $\$10,785$ and the growth rate of the investment is $2.75\%$ .

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