Question
The value of a saving account earning interest after a few years is given by the equation:
y=1500(1+0.02)^3
What does the 0.2 represent in the exponential equation? What is grow or decay factor?
A.
initial value; 1.20
B.
rate; 1.02
C.
time; 1.00
D.
base; 1.02
y=1500(1+0.02)^3
What does the 0.2 represent in the exponential equation? What is grow or decay factor?
A.
initial value; 1.20
B.
rate; 1.02
C.
time; 1.00
D.
base; 1.02
Answers
GPT-4o mini
In the equation \( y = 1500(1 + 0.02)^3 \):
- The \( 0.02 \) represents the rate of interest, which is 2% in this case.
- The quantity \( 1 + 0.02 = 1.02 \) serves as the base of the exponential expression, and it captures the growth factor.
To determine the correct answer for what \( 0.02 \) represents and what the growth factor is:
- **\( 0.02 \)** is indeed the rate.
- The growth factor (the base of the exponent representing how much the account balance increases) is **\( 1.02 \)**.
So the correct answer from your options is:
**B. rate; 1.02**
- The \( 0.02 \) represents the rate of interest, which is 2% in this case.
- The quantity \( 1 + 0.02 = 1.02 \) serves as the base of the exponential expression, and it captures the growth factor.
To determine the correct answer for what \( 0.02 \) represents and what the growth factor is:
- **\( 0.02 \)** is indeed the rate.
- The growth factor (the base of the exponent representing how much the account balance increases) is **\( 1.02 \)**.
So the correct answer from your options is:
**B. rate; 1.02**