Pretend the program in Senegal had been reducing infant mortality at a rate of 12.5 % per year. How long would it take for infant mortality to be reduced by 38 %?
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To calculate how long it would take for infant mortality to be reduced by 38%, we need to use the concept of logarithms and exponential decay. Here is the step-by-step explanation:
1. First, we need to convert the annual reduction rate of 12.5% to a decimal by dividing it by 100:
Conversion: 12.5% / 100 = 0.125
2. Next, we use the exponential decay formula to calculate the time it takes for the mortality rate to decrease by a certain percentage:
Formula: t = (ln(P0 / P)) / r
Where:
- t is the time taken (in years),
- P0 is the initial value (100%),
- P is the desired final value (100% - 38% = 62%),
- r is the rate of reduction (0.125).
3. Calculate the natural logarithm of the ratio P0 / P:
ln(100% / 62%) = ln(1.6129) ≈ 0.4762
4. Divide the result from step 3 by the rate of reduction:
t = 0.4762 / 0.125 ≈ 3.810
Therefore, it would take approximately 3.810 years for infant mortality to be reduced by 38% based on the annual reduction rate of 12.5% in Senegal.