Question

A biologist isolates two strains of a particular virus and monitors the growth of each, starting with samples of 0.02 grams. Strain A increases by 10% in 8 hours, and strain B increases by 13% in 11 hours.

(a) How much did the sample of strain A weigh after 8 hours?
(Round the answer to four decimal places. Your answer must include units.)
(b) What was the hourly growth factor for strain A?
(Round the answer to four decimal places.)
(c) How much did the sample of strain B weigh after 11 hours?
(Round the answer to four decimal places. Your answer must include units.)
(d) What was the hourly growth factor for strain B?
(Round the answer to four decimal places.)
(e) Which strain of virus grows more rapidly? A or B

Answer 1

After 8 hours, the sample of strain A weighs 0.022 grams. The hourly growth factor for strain A is 1.25%. After 11 hours, the sample of strain B weighs 0.0226 grams. The hourly growth factor for strain B is 1.1818%. Strain A grows more rapidly than strain B.

Step-by-step explanation:

(a) To calculate how much the sample of strain A weighs after 8 hours, we need to find the final weight by increasing the initial weight by 10%. We can use the formula:

Final weight = Initial weight + (Initial weight * growth rate)

Using the given values, the final weight = 0.02 + (0.02 * 0.1) = 0.022 grams.

(b) The hourly growth factor for strain A can be calculated by dividing the growth rate by the number of hours:

Hourly growth factor = 10% / 8 hours = 0.0125 or 1.25%.

(c) Similarly, to find the weight of strain B after 11 hours, we use the formula:

Final weight = Initial weight + (Initial weight * growth rate)

Using the given values, the final weight = 0.02 + (0.02 * 0.13) = 0.0226 grams.

(d) The hourly growth factor for strain B can be calculated by dividing the growth rate by the number of hours:

Hourly growth factor = 13% / 11 hours = 1.1818%.

(e) To compare the growth rates of strains A and B, we compare their hourly growth factors. Strain A has a growth factor of 1.25% while strain B has a growth factor of 1.1818%. Therefore, strain A grows more rapidly than strain B.