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?
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.