Question

Pleaseee someone help me :( Ive been stuck on this for an hour

Organisms A and B start out with the same population size.

Organism A's population doubles every day. After 5 days, the population stops growing and a virus cuts it in half every day for 3 days.

Organism B's population grows at the same rate but is not infected with the virus. After 8 days, how much larger is organism B's population than organism A's population? Answer the questions to find out.

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

Answer 1

factor 2^5

Explanation:

Answer 2

The number of times organism B's population is larger than organism A's population after 8 days is 32 times

Explanation:

The population of organism A doubles every day, geometrically as follows

a, a·r, a·r²

Where;

r = 2

The population after 5 days, is therefore;

Pₐ₅ = = 32·a

The virus cuts the population in half for three days as follows;

The first of ta·2⁵ he three days = 32/2 = 16·a

The second of the three days = 16/2 = 8·a

After the third day, Pₐ = 8/2 = 8·a

The population growth of organism B is the same as the initial growth of organism A, therefore, the population, P₈ of organism B after 8 days is given as follows;

P₈ = a·2⁸ = 256·a

Therefore, the number of times organism B's population is larger than organism A's population after 8 days is P₈/Pₐ = 256·a/8·a = 32 times

Which gives, the number of times organism B's population is larger than organism A's population after 8 days is 32 times.

Hope this helps you out! :)

Also, it's OK! This was actually pretty hard to figure out!