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?
To find the value of the quantity after 28 days, we first need to convert 28 days to weeks. Since there are 7 days in a week, 28 days is equivalent to 4 weeks.
Next, we can use the continuous decay formula:
A = A0 * e^(rt)
Where:
A = final value of the quantity
A0 = initial value of the quantity
e = Euler's number (~2.71828)
r = decay rate
t = time in weeks
Plugging in the values we have:
A = 790 * e^(-0.35*4)
A = 790 * e^(-1.4)
A = 790 * 0.2466
A = 194.99
Therefore, the value of the quantity after 28 days is approximately 195.00 to the nearest hundredth.