Question

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.

Answer 1

Answer:

Let's calculate the population sizes of organisms A and B step by step.

Step-by-step explanation:

**Organism A:**

- Population doubles every day for 5 days.

- After 5 days, the population stops growing and then is halved by a virus for 3 days.

Starting population of A = 1 (let's assume 1 for simplicity).

1. Day 1: Population = 1 × 2 = 2

2. Day 2: Population = 2 × 2 = 4

3. Day 3: Population = 4 × 2 = 8

4. Day 4: Population = 8 × 2 = 16

5. Day 5: Population = 16 × 2 = 32

Now, the virus starts halving the population:

6. Day 6: Population = 32 ÷ 2 = 16

7. Day 7: Population = 16 ÷ 2 = 8

8. Day 8: Population = 8 ÷ 2 = 4

So, after 8 days, organism A's population is 4.

**Organism B:**

- Population doubles every day for 8 days.

Starting population of B = 1 (same assumption as above).

1. Day 1: Population = 1 × 2 = 2

2. Day 2: Population = 2 × 2 = 4

3. Day 3: Population = 4 × 2 = 8

4. Day 4: Population = 8 × 2 = 16

5. Day 5: Population = 16 × 2 = 32

6. Day 6: Population = 32 × 2 = 64

7. Day 7: Population = 64 × 2 = 128

8. Day 8: Population = 128 × 2 = 256

So, after 8 days, organism B's population is 256.

**Comparison:**

Now we compare the populations of organism A and organism B after 8 days:

Population of A = 4

Population of B = 256

Therefore, organism B's population is larger than organism A's population by \(256 - 4 = 252\) organisms.

Hence, after 8 days, organism B's population is 252 organisms larger than organism A's population.

Answer 2

Answer: Organism B's population is 252 times larger

Step-by-step explanation:

Let's break down the growth of both organisms:

For Organism A:

- Population doubles every day for 5 days.

- Then, a virus cuts the population in half every day for 3 days.

For Organism B:

- Population doubles every day for 8 days.

Let's calculate the populations for both organisms:

For Organism A:

- After 5 days, the population doubles 5 times, so the population is \(2^5 = 32\).

- After the virus cuts the population in half every day for 3 days, the population becomes \(32 \times (0.5)^3 = 4\).

For Organism B:

- The population doubles every day for 8 days, so the population is \(2^8 = 256\).

Now, we can compare the populations:

Organism B's population is \(256 - 4 = 252\) larger than Organism A's population.

So, Organism B's population is 252 times larger than Organism A's population after 8 days.