The equation

Question

𝑦
=
650
(
0.95
)
𝑡
y=650(0.95)
t
represents the decay of the number of flu bacteria in the body after beginning treatment. What is the rate of decay?

(2 points)

○ The rate of decay is 95%

○ The rate of decay is 0.05%

○ The rate of decay is 5%

○ The rate of decay is 32.5

Answer 1

The equation \( y = 650(0.95)^t \) represents exponential decay, where \( 0.95 \) is the base that indicates how the quantity \( y \) decreases over time \( t \).

To find the rate of decay, you can look at the percentage decrease in the quantity. Since the base \( 0.95 \) shows that the quantity is multiplied by \( 0.95 \) each time period, we can deduce the decay rate as follows:

1. The quantity decreases to 95% of its previous value (hence the \( 0.95 \)).
2. This means that \( 100% - 95% = 5% \) of the quantity is lost each time period.

Therefore, the rate of decay is \( \text{5%} \).

So the correct answer is:

○ The rate of decay is 5%.