Question
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?
Answers
GPT 3.5
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.
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.