Question

In 2015 there was 57 232 babies born. How many babies will be born in the next 12 years time in total, if we assume the birth rate will drop 1% each year? The year 2015 is the first year in the 12 years. Give me the answer using geometric sum.

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To calculate the total number of babies born in the next 12 years using geometric sum, we need the initial number of babies born in 2015, which is 57,232.

Given that the birth rate drops 1% each year, this means the number of babies born each year will decrease by 1% of the previous year's number.

Let's denote the number of babies born in the first year after 2015 asx , then the number of babies born in the second year will be 0.99x , in the third year will be 0.99^2x , and so on.

The total number of babies born in the next 12 years will be the sum of a geometric series with 12 terms, starting with 57,232 babies and a common ratio of 0.99.

The formula for the sum of a geometric series is given by:

S = a \cdot \frac{1 - r^n}{1 - r}

where:

S is the total sum,

a is the first term,

r is the common ratio, and

n is the number of terms.

Substitutea = 57,232 , r = 0.99 , and n = 12 into the formula:

S = 57232 \cdot \frac{1 - 0.99^{12}}{1 - 0.99}

S=57232\cdot\frac{1-0.8863848717}{0.01}

S=57232\cdot\frac{0.1136151283}{0.01}

S=57232\cdot11.36151283

S=650,242.1022

Therefore, the total number of babies born in the next 12 years will be\boxed{650,242} .

Given that the birth rate drops 1% each year, this means the number of babies born each year will decrease by 1% of the previous year's number.

Let's denote the number of babies born in the first year after 2015 as

The total number of babies born in the next 12 years will be the sum of a geometric series with 12 terms, starting with 57,232 babies and a common ratio of 0.99.

The formula for the sum of a geometric series is given by:

where:

Substitute

Therefore, the total number of babies born in the next 12 years will be

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