Question

the number of bacteria in a growth medium is expected to increase by 150% every 2 hours during a period of observation. the number of bacteria in the growth medium was estimated to be 7,000 when the period of observation began. which function p gives the expected number of bacteria in this growth medium t hours after the period of observation began?
a. p(t)=7,000(1.50)^{\frac{t}{2}}
b. p(t)=7,000(1.50)^{2t}
c. p(t)=7,000(2.50)^{\frac{t}{2}}
d. p(t)=7,000(2.50)^{2t}

Explanation:

Step1: Calculate growth - factor

Initial amount is 7000. A 150% increase means new amount is 1 + 1.5=2.5 times the previous.

Step2: Determine exponent

Growth occurs every 2 hours. In t hours, number of 2 - hour intervals is $\frac{t}{2}$.

Step3: Form function

The function is $P(t)=7000(2.50)^{\frac{t}{2}}$.

Answer:

c. $P(t)=7,000(2.50)^{\frac{t}{2}}$