Question

A center for disease control is releasing a particular bacteria. They determined after 10 hours, the population of bacteria becomes 10,000 times larger. If the initial amount was 30, what was the population of the bacteria in 5 hours?

a) 500
b) 600
c) 700
d) 800

Answer 1

The growth of bacteria is exponential. By finding the hourly growth rate and applying it to the initial amount of bacteria over 5 hours, the population is determined to be 600, which is option b).

Step-by-step explanation:

The exponential growth of bacteria suggests that the population doubles over a specific period. The center for disease control indicated the bacteria's population becomes 10,000 times larger after 10 hours, which implies that the growth rate is consistent and can be described by an exponential function.

Since we're looking at a scenario that occurs in half the time given for the 10,000-fold increase, we need to calculate the population after 5 hours. We can find the growth rate by taking the tenth root (since 10 hours) of 10,000 to find the increase per hour and then raise this to the fifth power for the 5-hour growth.

If we let 'r' be the growth rate per hour, 10,000 is equal to r10. Therefore, r = 10,0001/10. After 5 hours, the population is 30 × r5. When we calculate this value, we find the population after 5 hours to be 600 bacteria, which corresponds to option b).