Answer:
5,035,041
Step-by-step explanation:
Exponential growth:
[tex] y = a(1 + r)^{x} [/tex]
y = future amount
a = initial amount
r = growth rate
x = number of periods
Part A: growth at the rate of doubling each 15 minutes for 274 minutes
Each period is 15 minutes.
a = 37
x = 274/15 = number of periods
r = 100%
[tex] y = 37(1 + 1)^{\frac{274}{15} [/tex]
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Exponential decay:
[tex] y = a(1 - r)^{x} [/tex]
The growth takes place from 9 AM for 274 minutes, or 4 hours and 34 minutes, until 1:34 PM. The decay goes from 1:34 PM to 7 PM, or 5 hours and 26 minutes, or 326 minutes
Part B: decay at the rate of 6% each 24 minutes for 326 minutes
[tex]y = 37(1 + 1)^{\frac{274}{15}}(1 - 0.06)^{\frac{326}{24}}[/tex]
[tex] y = 5035041 [/tex]
Answer: 5,035,041
