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Calculate the doubling time.

Given:
[tex]\[
\frac{70}{r (\text{growth rate})} = \text{Doubling Time}
\][/tex]
where [tex]\( r (\text{growth rate}) = 10\% \)[/tex]

Options:
A. 1000 years
B. 7 years
C. 70 years

Sagot :

GinnyAnswer
To calculate the doubling time, we use the formula:

[tex]\[ \text{Doubling Time} = \frac{70}{\text{growth rate}} \][/tex]

Given that the growth rate is 10% per year:

[tex]\[ \text{growth rate} = 10\% \][/tex]

First, convert the percentage to a decimal for ease of calculation:

[tex]\[ 10\% = 0.10 \][/tex]

However, since we are using the rule of 70, we can directly use the percentage value without converting it to a decimal.

Substitute the growth rate into the formula:

[tex]\[ \text{Doubling Time} = \frac{70}{10} \][/tex]

Perform the division:

[tex]\[ \frac{70}{10} = 7 \][/tex]

So, the doubling time is:

[tex]\[ 7 \text{ years} \][/tex]

Therefore, among the given options:

1. 1000 years
2. 7 years
3. 70 years

The correct answer is:

[tex]\[ 7 \text{ years} \][/tex]
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