Question

PLEASE, I NEED THIS DONE!!!!!!!!! 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. (2 points)


2. The expression showing organism A's decrease in population over the next 3 days is

(

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. (2 points)


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. (2 points)


4. Write an exponential expression showing organism B's increase in population over the same 8 days. (2 points)


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. (2 points)

Answer 1

Let's break down the problem step by step:

1. By what factor does organism A's population grow in the first five days?

Organism A's population doubles every day for 5 days. So, the factor by which it grows can be expressed as 2^5 since it doubles 5 times. This simplifies to 32.

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

(2–1)^3 is equivalent to 1^3, which is simply 1.

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

In the first 5 days, the population grows by a factor of 32, and then it decreases by a factor of (1/2)^3 during the next 3 days. So, the total change in organism A's population after 8 days can be expressed as 32 * (1/2)^3.

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

Organism B's population also doubles every day for 8 days. So, the factor by which it grows can be expressed as 2^8, which is 256.

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.

To find how many times greater organism B's population is than organism A's population, divide the growth factor of B by the total change factor of A:

Organism B's population / Organism A's population = 256 / (32 * (1/2)^3)

Now, simplify this expression step by step:

Organism B's population / Organism A's population = 256 / (32 * (1/8))

Next, simplify the denominator:

Organism B's population / Organism A's population = 256 / (4)

Finally, divide to get the answer:

Organism B's population / Organism A's population = 64

So, organism B's population is 64 times greater than organism A's population after 8 days.

Explanation: