Question

Two different strains of cold virus were isolated and put in cultures to grow. Virus A triples every 8 h while virus B doubles every 4.8 h. If each culture has 1000 viruses to start, which has more after 24 h ? The exponential function is P=C(a) ᵗ

Answer 1

After 24 hours, virus B has significantly more viruses than virus A. Virus A has 27,000 viruses (triples every 8 hours), and virus B has 32,000 viruses (doubles every 4.8 hours).

Step-by-step explanation:

To determine which virus culture ends up with more viruses after 24 hours, we can use the provided exponential growth formula P = C(a)⁴, where P represents the final number of viruses, C is the initial number of viruses, a is the growth multiple per time period, and t is the number of time periods.

For virus A, which triples every 8 hours, the growth multiple (a) is 3. Since the time period is 24 hours, which is three 8-hour periods, t will be 3. So, the calculation for virus A is P = 1000(3)³ = 1000 × 27 = 27,000 viruses after 24 hours.

For virus B, which doubles every 4.8 hours, the growth multiple (a) is 2. Since the time period is 24 hours, we will have t as 24 ÷ 4.8 = 5 time periods. The calculation for virus B is P = 1000(2)⁵ = 1000 × 32 = 32,000 viruses after 24 hours.

After comparing the two results, virus B, with 32,000 viruses, has viruses than virus A after 24 hours.