A quantity with an initial value of 660 grows exponentially at a rate of 6.5% every 9 minutes. What is the value of the quantity after 324 seconds, to the nearest hundredth?

Answer 1

To find the value of the quantity after 324 seconds, we first need to convert 324 seconds to minutes:

324 seconds / 60 seconds/minute ≈ 5.4 minutes

Now we can calculate the value of the quantity after 5.4 minutes using the formula for exponential growth:

A = P(1 + r)^t

Where:
A = final amount
P = initial amount (660)
r = growth rate per period (6.5% or 0.065)
t = number of periods (5.4 minutes / 9 minutes = 0.6 periods)

Plug in the values and calculate:

A = 660(1 + 0.065)^0.6
A = 660(1.065)^0.6
A ≈ 660(1.03952)
A ≈ 686.63

Therefore, the value of the quantity after 324 seconds is approximately 686.63 to the nearest hundredth.