Question

58.(A) (5pts)A certain type of bacteria, given favorable growth medium, quadruples in population every 6 hours. Given that there were 150 bacteria to start with, how many bacterial will there be in two and a half days? (Give the EXACT answer... i.e. do not roun

Answer 1

Answer:

157286400 bacteria

Step-by-step explanation:

We are given the following in the question:

The bacteria increases 4 times every 6 hours.

Initially there are 150 bacteria.

Thus, we can write the function for number of bacteria after x hours,

$f(x) = 150(4)^{\frac{x}{6}}$

We have to find the number of bacteria in 2.5 days.

1 day = 24 hours

Thus,

$2.5\text{ days} = 24\times 2.5 = 60\text{ hours}$

Putting x = 60 in the above equation, we get,

$f(60) = 150(4)^{\frac{60}{6}} = 150(4)^{10} = 157286400$

Thus, there will be 157286400 bacteria in two and a half days.