Question

Organisms A and B start out with the same population size. Organism A’s population doubles every day. After five days, the population stops growing and a virus cuts it in half every day for three days. Organism bees population grows at the same rate but it’s not infected with the virus. After eight days how much larger is organism B’s population an organism A’s population?

1: By what factor does organism as population grow in the first five days? Express your answer as an exponential expression

Answer 1

factor 2^5

Explanation:

Answer 2

1. 252N = (
`2^(2)` x
`3^(2)` x
`7^(1)`)N

2. Factor =
`2^(5)`

Explanation:

Let the starting population size for organisms A and B be represented by N.

For organism A;

Day 0: N

Day 1: 2N

Day 2:
`2^(2)`N

Day 3:
`2^(3)`N

Day 4:
`2^(4)`N

Day 5:
`2^(5)`N

Day 6:
`2^(4)`N

Day 7:
`2^(3)`N

Day 8:
`2^(2)`N

For organism B;

Day 0: N

Day 1: 2N

Day 2:
`2^(2)`N

Day 3:
`2^(3)`N

Day 4:
`2^(4)`N

Day 5:
`2^(5)`N

Day 6:
`2^(6)`N

Day 7:
`2^(7)`N

Day 8:
`2^(8)`N

1. After the eight days, organism B's population is larger than organism A's population by;

`2^(8)`N -
`2^(2)`N = 256N - 4N

= 252N

= (
`2^(2)` x
`3^(2)` x
`7^(1)`)N

2. Organism A's population grows by
`2^(5)`.