Answer:
The value of the quantity after 144 hours is 19,200.
Step-by-step explanation:
Let the quantity to be found be P(t) where t is the time in hours
Let [tex]P_0[/tex] be the initial amount. Therefore [tex]P_0[/tex] = 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) = [tex]P_0 \times ( 2^{\frac{t}{48} })[/tex] 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 × [tex]2^{(\frac{144}{48} )}[/tex] = [tex]2400 \times 2^{2}[/tex] = 2400 × 8 = 19200.
