Questions: (a) Convert the growth rate 2.5% to a decimal. (Enter your answer as a decimal.) (b) Convert the growth rate 0.6 to a percent. (Enter your answer as a percent.) (c) A population of 1000 organisms is growing at a rate of 2.5% per year. How many organisms will there be after 3 years? (Round your answer to the nearest whole number.) (d) If a population increases from 500 to 800 over a 10-year period, what is the growth rate? (Enter your answer as a percent rounded to one decimal place.) (e) A population grows from 1000 to 1500 in 5 years. What is the annual growth rate? (Enter your answer as a percent rounded to one decimal place.) (f) A population of bacteria doubles every 12 hours. What is the growth rate? (Enter your answer as a percent rounded to one decimal place.) (g) The number of cells in a petri dish increases from 100 to 400 in 2 days. What is the daily growth rate? (Enter your answer as a percent rounded to one decimal place.) (h) If a population grows at a rate of 3% per year, how long will it take for the population to double? (Round your answer to the nearest whole number of years.)

(a) Convert the growth rate 2.5% to a decimal. (Enter your answer as a decimal.) (b) Convert the growth rate 0.6 to a percent. (Enter your answer as a percent.) (c) A population of 1000 organisms is growing at a rate of 2.5% per year. How many organisms will there be after 3 years? (Round your answer to the nearest whole number.) (d) If a population increases from 500 to 800 over a 10-year period, what is the growth rate? (Enter your answer as a percent rounded to one decimal place.) (e) A population grows from 1000 to 1500 in 5 years. What is the annual growth rate? (Enter your answer as a percent rounded to one decimal place.) (f) A population of bacteria doubles every 12 hours. What is the growth rate? (Enter your answer as a percent rounded to one decimal place.) (g) The number of cells in a petri dish increases from 100 to 400 in 2 days. What is the daily growth rate? (Enter your answer as a percent rounded to one decimal place.) (h) If a population grows at a rate of 3% per year, how long will it take for the population to double? (Round your answer to the nearest whole number of years.)
Transcript text: (a) Convert the growth rate 2.5% to a decimal. (Enter your answer as a decimal.) (b) Convert the growth rate 0.6 to a percent. (Enter your answer as a percent.) (c) A population of 1000 organisms is growing at a rate of 2.5% per year. How many organisms will there be after 3 years? (Round your answer to the nearest whole number.) (d) If a population increases from 500 to 800 over a 10-year period, what is the growth rate? (Enter your answer as a percent rounded to one decimal place.) (e) A population grows from 1000 to 1500 in 5 years. What is the annual growth rate? (Enter your answer as a percent rounded to one decimal place.) (f) A population of bacteria doubles every 12 hours. What is the growth rate? (Enter your answer as a percent rounded to one decimal place.) (g) The number of cells in a petri dish increases from 100 to 400 in 2 days. What is the daily growth rate? (Enter your answer as a percent rounded to one decimal place.) (h) If a population grows at a rate of 3% per year, how long will it take for the population to double? (Round your answer to the nearest whole number of years.)
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Solution

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Solution Steps

Here are the solutions for the first three questions:

Step 1: Convert the x interval, 4.5 < x, to a z interval

Given that x (RBC count) has a mean (μ) of 4.7 and a standard deviation (σ) of 0.2, we can convert an x value to a z-score using the z-score formula:

z = (x - μ) / σ

For x = 4.5:

z = (4.5 - 4.7) / 0.2
z = -1

So, the z interval corresponding to 4.5 < x is z > -1.

Step 2: Convert the x interval, x < 4.2, to a z interval

Using the same z-score formula and the given mean and standard deviation:

For x = 4.2:

z = (4.2 - 4.7) / 0.2
z = -2.5

Therefore, the z interval corresponding to x < 4.2 is z < -2.5.

Step 3: Convert the x interval, 4.0 < x < 5.5, to a z interval

We need to convert both x values to their respective z-scores.

For x = 4.0:

z = (4.0 - 4.7) / 0.2
z = -3.5

For x = 5.5:

z = (5.5 - 4.7) / 0.2
z = 4

Thus, the z interval corresponding to 4.0 < x < 5.5 is -3.5 < z < 4.

Final Answer:

(a) z > -1 (b) z < -2.5 (c) -3.5 < z < 4

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