A quantity with an initial value of 8200 grows continuously at a rate of 0.55% per decade. What is the value of the quantity after 97 years, to the nearest hundredth?
To solve this problem, we can use the formula for continuous growth:
A = P * e^(rt)
Where:
A = final amount
P = initial amount
e = Euler's number (approximately 2.71828)
r = growth rate per year (0.55% or 0.0055)
t = time in years (97)
Plugging in the values we have:
A = 8200 * e^(0.0055 * 97)
A = 8200 * e^(0.5335)
A ≈ 8200 * 1.7067
A ≈ 13974.92
Therefore, the value of the quantity after 97 years, to the nearest hundredth, is approximately $13974.92.