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.

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2. The expression showing organism A's decrease in population over the next 3 days is
(\small {\frac{1}{2}})^3
(
2
1

)
3
. This can be written as (2–1)3.

Write (2–1)3 with the same base but one exponent.

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3. By combining the increase and decrease, find an exponential expression for the total change in organism A's population after 8 days. Show your work.

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4. Write an exponential expression showing organism B's increase in population over the same 8 days.

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5. Use your answers to questions 3 and 4 to write an expression for how many times greater organism B's population is than organism A's population after 8 days.
Simplify your expression, then write it as a number that is not in exponential form. Show your process.

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