Question

a quantity with an initial value of 380 decays continuously at a rate of 0.5% per minute. what is the value of the quantity after 69 seconds, to the nearest hundredth?
answer

Explanation:

Step1: Convert time to minutes

69 seconds is $\frac{69}{60} = 1.15$ minutes.

Step2: Use continuous decay formula

The formula for continuous decay is $A = P e^{rt}$, where $P$ is the initial amount, $r$ is the rate (in decimal), and $t$ is time. Here, $P = 380$, $r = -0.005$ (since it's decay, rate is negative), and $t = 1.15$.
So $A = 380 \times e^{-0.005 \times 1.15}$.
First calculate the exponent: $-0.005 \times 1.15 = -0.00575$.
Then $e^{-0.00575} \approx 0.99427$.
Multiply by 380: $380 \times 0.99427 \approx 377.82$.

Answer:

377.82