Question

A quantity with an initial value of 620 grows continuously at a rate of 0.3% per second. What is the value of the quantity after 0.5 minutes, to the nearest hundredth?

Answer 1

To calculate the value of the quantity after 0.5 minutes, we first need to convert the time to seconds:

0.5 minutes * 60 seconds/minute = 30 seconds

Next, we use the formula for continuous growth:

A = P * e^(rt)

Where:
A = final value of the quantity
P = initial value of the quantity (620)
e = Euler's number (approximately 2.71828)
r = growth rate per second (0.3% or 0.003)
t = time in seconds (30 seconds)

Plugging in the values:

A = 620 * e^(0.003 * 30)
A = 620 * e^(0.09)
A ≈ 620 * 1.093871

A ≈ 677.95

Therefore, the value of the quantity after 0.5 minutes is approximately 677.95 to the nearest hundredth.