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?
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.