Answer :
To determine the percent rate of change from the given expression [tex]\(45 \cdot (1 - 0.60)^{2x}\)[/tex], we should carefully analyze the components of the expression.
1. Identify the base of the exponent:
The expression inside the exponent is [tex]\(1 - 0.60\)[/tex]. Simplifying this, we get:
[tex]\[ 1 - 0.60 = 0.40 \][/tex]
So the base of the exponent [tex]\(2x\)[/tex] is [tex]\(0.40\)[/tex].
2. Determine the percent rate of change:
The percent rate of change is derived from how much the base deviates from 1. The deviation percentage can be calculated by the difference between 1 and the base (0.40 in this case), and then expressing that difference as a percentage.
- Calculate the difference:
[tex]\[ 1 - 0.40 = 0.60 \][/tex]
- Express this as a percentage:
[tex]\[ 0.60 \times 100 = 60\% \][/tex]
Thus, the percent rate of change for the given expression [tex]\(45 \cdot (1 - 0.60)^{2x}\)[/tex] is [tex]\(60\%\)[/tex]. Therefore, the correct answer is:
[tex]\[ \boxed{60\%} \][/tex]
1. Identify the base of the exponent:
The expression inside the exponent is [tex]\(1 - 0.60\)[/tex]. Simplifying this, we get:
[tex]\[ 1 - 0.60 = 0.40 \][/tex]
So the base of the exponent [tex]\(2x\)[/tex] is [tex]\(0.40\)[/tex].
2. Determine the percent rate of change:
The percent rate of change is derived from how much the base deviates from 1. The deviation percentage can be calculated by the difference between 1 and the base (0.40 in this case), and then expressing that difference as a percentage.
- Calculate the difference:
[tex]\[ 1 - 0.40 = 0.60 \][/tex]
- Express this as a percentage:
[tex]\[ 0.60 \times 100 = 60\% \][/tex]
Thus, the percent rate of change for the given expression [tex]\(45 \cdot (1 - 0.60)^{2x}\)[/tex] is [tex]\(60\%\)[/tex]. Therefore, the correct answer is:
[tex]\[ \boxed{60\%} \][/tex]
