Problem

Complete the following table.
Population Growth Rate, $\mathbf{k}$ Doubling Time, $\mathrm{T}$
Country A $2.2 \%$ per year
Country B
46 years

Population Growth Rate, $\mathbf{k}$ Doubling Time, $T$

Country A $2.2 \%$ per year $\square$ years
Country B $\quad$ B Ber year 46years
(Round doubling time to the nearest whole number and round growth rate to the nearest tenth.)

Answer

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Answer

The final answer is: The doubling time for Country A is \(\boxed{32}\) years and the growth rate for Country B is \(\boxed{1.5\%}\) per year.

Steps

Step 1 :The problem is asking to find the doubling time for Country A and the growth rate for Country B. The doubling time and the growth rate are related by the formula: \(T = \frac{70}{k}\) where \(T\) is the doubling time and \(k\) is the growth rate.

Step 2 :For Country A, we know the growth rate \(k = 2.2\% = 2.2\) (in the formula, we use the growth rate as a whole number, not a percentage). We can substitute this into the formula to find the doubling time.

Step 3 :For Country B, we know the doubling time \(T = 46\) years. We can substitute this into the formula to find the growth rate.

Step 4 :Let's calculate these values.

Step 5 :Substituting \(k = 2.2\) into the formula \(T = \frac{70}{k}\), we get \(T = \frac{70}{2.2} = 32\) years for Country A.

Step 6 :Substituting \(T = 46\) into the formula \(T = \frac{70}{k}\), we get \(k = \frac{70}{46} = 1.5\%\) per year for Country B.

Step 7 :The final answer is: The doubling time for Country A is \(\boxed{32}\) years and the growth rate for Country B is \(\boxed{1.5\%}\) per year.

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