Answer :
The exponential function that describes the situation is Option C. f(t) = 66 × 0.995^t, representing a 0.5% weekly decrease from an initial value of 66.
To find the exponential function that satisfies an initial value of 66 and decreases at a rate of 0.5% per week, we start by establishing the general form of an exponential decay function: f(t) = A × (rate)^t. Here, the initial value A is 66, and since the function decreases by 0.5% each week, the decay rate is 1 - 0.005 = 0.995.
Thus, the exponential function can be written as:
Option C. f(t) = 66 × 0.995^t
This function reflects a weekly decrease of 0.5% from an initial value of 66.
Complete question:
Find the exponential function that satisfies the given conditions.
Initial value = 66, decreasing at a rate of 0.5% per week
A. f(t) = 0.5 ⋅ 0.34t
B. f(t) = 66 ⋅ 1.5t
C. f(t) = 66 ⋅ 0.995t
D. f(t) = 66 ⋅ 1.005t
Answer:
f(t) = 66·0.995^t
Step-by-step explanation:
You can try t=0 and t=1 in each of the formulas to see which one gives values of 66 and 0.5% less than 66, or 65.67.
The first function has an initial value of 0.5, so is not correct.
The second function gives f(1) = 99, so is not correct.
The third function gives f(1) = 65.67, so is correct.
The fourth function gives f(1) = 66.33, so is not correct.
_____
You can realize that the multiplier will be 0.5% less than 100%, so will be 99.5% = 0.995. This number shows up only in the third selection.
