Question

A quantity with an initial value of 2400 grows exponentially at a rate such that the quantity doubles every 2 days. What is the value of the quantity after 144 hours, to the nearest hundredth

Answer 1

The value of the quantity after 144 hours is 19,200.

Explanation:

Let the quantity to be found be P(t) where t is the time in hours

Let
`P_0` be the initial amount. Therefore
`P_0` = 2400.

The amount doubles every 2 days. The equivalent of 2 days is 48 hours

So the equation that can model the given data will be given by

P(t) =
`P_0 * ( 2^{(t)/(48) })` where t is the time in hours.

We divide the time t by 48 to find out how many time does the quantity actually double.

Therefore the value of the quantity after 144 hours is ,

P(144) = 2400 ×
`2^{((144)/(48) )}` =
`2400 * 2^(2)` = 2400 × 8 = 19200.