Question

a quantity with an initial value of 790 decays continuously at a rate of 35% per week. what is the value of the quantity after 28 days, to the nearest hundredth?

Explanation:

Step1: Convert time to weeks

28 days is equal to $\frac{28}{7} = 4$ weeks.

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 of decay (in decimal), and $t$ is the time. Here, $P = 790$, $r = - 0.35$ (negative because it's decay), and $t = 4$.
So, $A = 790\times e^{-0.35\times4}$

Step3: Calculate the exponent

First, calculate $-0.35\times4=-1.4$

Step4: Calculate the value of $e^{-1.4}$

$e^{-1.4}\approx0.2466$

Step5: Calculate the final amount

$A = 790\times0.2466\approx194.81$

Answer:

194.81