QuestionThe graph of the equation representing compound interest is that of: A. linear function. B. quadratic function. C. exponential function. D. None of the above

Studdy Solution

STEP 1

1. Compound interest is calculated using the formula $A = P(1 + r/n)^{nt}$ , where $A$ is the amount of money accumulated after n years, including interest.
2. $P$ is the principal amount (the initial amount of money).
3. $r$ is the annual interest rate (in decimal form).
4. $n$ is the number of times that interest is compounded per year.
5. $t$ is the time the money is invested for in years.

STEP 2

1. Understand the form of the compound interest equation.
2. Identify the type of function based on the equation form.

STEP 3

The compound interest formula is given by:
$A = P(1 + r/n)^{nt}$
This formula represents the amount $A$ as a function of time $t$ .

STEP 4

Identify the type of function:
- The equation $A = P(1 + r/n)^{nt}$ has the variable $t$ in the exponent. - Functions where the variable is in the exponent are known as exponential functions.
Therefore, the graph of the equation representing compound interest is that of an exponential function.
The correct answer is $\boxed{\text{C. exponential function}}$ .

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