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. The expression showing organism A's decrease in population over the next 3 days is ( 1 2 ) ( 2 1 ​ ) 3 . This can be written as (2–1)3. Write (2–1)3 with the same base but one exponent.

Answer:

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

Step-by-step 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.

Final answer:

Organism A's population at the end of 5 days is 2^5. After 5 days, a virus cuts it in half for 3 days. Organism B's population at the end of 8 days is 2^8. To find the difference, subtract organism A's population from organism B's population.

Explanation:

Organism A's population doubles every day for 5 days, so the population at the end of 5 days is 25. After 5 days, a virus cuts the population in half for 3 days, so we need to find (25) * (2-1)3. Using the rule of exponents, we can rewrite this expression as (25+(-1*3)), which simplifies to 2-4.

Organism B's population grows at the same rate but is not infected with the virus. After 8 days, the population is 28.

To find out how much larger organism B's population is than organism A's population, we need to subtract the population of organism A from organism B. So, 28 - 2-4 is the answer.

Learn more about Population growth and virus impact here:

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