A program in Senegal has been reducing infant mortality at a rate
of 11.1% per year. How long will it take for infant mortality
to be reduced by 33%?
solve
.67 = 1(.889)^n
ln .67 = ln (.889^n)
ln .67 = n ln (.889)
n = ln .67/ln .889 = 3.4 years
thank you!
To determine how long it will take for infant mortality to be reduced by 33%, we can use the concept of exponential decay.
First, let's interpret the given rate of 11.1% per year as a decay rate. This means that infant mortality is decreasing by 11.1% each year. To convert this to a decay factor, we subtract the decay rate from 100%:
Decay factor = 100% - 11.1% = 88.9%
Next, we need to find out how many times we need to apply this decay factor to reduce the infant mortality by 33%. To do this, we can use the following formula for exponential decay:
Final Value = Initial Value * Decay Factor ^ Number of Periods
Let's assume the initial value is 100% (representing the current infant mortality rate), and we want to reduce it by 33%. Therefore, the final value will be 100% - 33% = 67%.
Using the above formula, we can rewrite it as:
0.67 = 1 * 0.889 ^ Number of Periods
To isolate the number of periods, we can take the logarithm of both sides of the equation. Since we want to find the time in years, we'll use the natural logarithm (ln):
ln(0.67) = Number of Periods * ln(0.889)
Now we can solve for the number of periods:
Number of Periods = ln(0.67) / ln(0.889)
Using a calculator, we can evaluate both logarithms and divide them to find the number of periods.
Number of Periods ≈ -2.005 / -0.1167 ≈ 17.17
Since we're dealing with time in years, we can round the number of periods up to the nearest whole number. Therefore, it would take approximately 18 years for infant mortality to be reduced by 33% based on the given rate of 11.1% per year.