Find the exponential function that satisfies the given conditions.
-Initial value $= 53$, decreasing at a rate of $0.48 \%$ per week
A) $f ( t ) = 0.48 \cdot 0.47 ^ { t }$
B) $f ( t ) = 53 \cdot 1.0048 ^ { t }$
C) $f ( t ) = 53 \cdot 1.48 ^ { t }$
D) $f ( t ) = 53 \cdot 0.9952 ^ { t }$

Question

Quizplus · Accepted Answer

The correct exponential function for a quantity that starts at an initial value and decreases by a certain percentage over time is given by $f(t) = \text{initial value} \cdot (1 - \text{rate of decrease})^t$. Since the rate of decrease is $0.48\%$, we subtract this from 1 (as a decimal, so $0.48\% = 0.0048$), giving $1 - 0.0048 = 0.9952$. Therefore, the function is $f(t) = 53 \cdot 0.9952^t$.

Find the Exponential Function That Satisfies the Given Conditions =53= 53=53

Find the Exponential Function That Satisfies the Given Conditions $= 53$