Find the exponential function that satisfies the given conditions.
-Initial value $= 55$, decreasing at a rate of $0.46 \%$ per week
A) $f ( t ) = 55 \cdot 1.0046 ^ { t }$
B) $f ( t ) = 0.46 \cdot 0.45 ^ { t }$
C) $\mathrm { f } ( \mathrm { t } ) = 55 \cdot 0.9954 ^ { \mathrm { t } }$
D) $f ( t ) = 55 \cdot 1.46 ^ { t }$

Question

Quizplus · Accepted Answer

The correct exponential function for a quantity that starts at 55 and decreases at a rate of 0.46% per week is $f(t) = 55 \cdot 0.9954^t$. This is because a decrease of 0.46% means the quantity retains 99.54% (100% - 0.46% = 99.54%) of its value each week, which is represented by the factor 0.9954.

Find the Exponential Function That Satisfies the Given Conditions =55= 55=55

Find the Exponential Function That Satisfies the Given Conditions $= 55$