An innovative rural public health program is reducing infant mortality in a certain West African country. Pretend the program in Senegal has been reducing infant mortality at a rate 8.1 % per year. How long will it take for infant mortality to be reduced by 30 %?
100 - 8.1 = 91.9
so each year number = .919 of year before
how many years before amount = 0.7 * original?
.7 = .919^n
log .7 = n log .919
-.1549 = n (-.03668)
n = 4.22 years
To determine how long it will take for infant mortality to be reduced by 30% in Senegal's rural public health program, we can follow these steps:
Step 1: Calculate the annual reduction in infant mortality
The program is reducing infant mortality at a rate of 8.1% per year. Therefore, the reduction in infant mortality each year is 8.1%.
Step 2: Calculate the reduction in infant mortality over the desired period (30%)
To find out how long it will take to achieve a 30% reduction in infant mortality, we need to divide 30% by the annual reduction rate of 8.1%.
30% / 8.1% = 3.7037
Step 3: Convert the decimal value to the nearest whole number
To get a more practical answer, we'll round up the result from the previous step to the nearest whole number.
Rounding up 3.7037 to the nearest whole number gives us 4.
Therefore, it will take approximately 4 years for the rural public health program in Senegal to reduce infant mortality by 30%.
To find out how long it will take for infant mortality to be reduced by 30%, we can use the concept of compound interest formula:
A = P(1 + r/n)^(n*t)
Where:
A = final amount (in this case, the final reduction in infant mortality percentage)
P = initial amount (100%)
r = annual percentage rate of reduction (8.1%)
t = time in years
n = number of times the interest is compounded per year (assuming it is compounded annually, n = 1 in this case)
Let's substitute the given values into the formula:
30 = 100(1 + 8.1/100)^(1*t)
Now, let's solve for t:
(1 + 8.1/100)^(t) = 30/100
(1 + 8.1/100)^(t) = 0.3
To solve for t, we need to take the logarithm of both sides of the equation. Let's use the natural logarithm (ln) in this case:
ln[(1 + 8.1/100)^(t)] = ln(0.3)
t * ln(1 + 8.1/100) = ln(0.3)
t = ln(0.3) / ln(1 + 8.1/100)
Using a calculator, we can find that:
t ≈ 6.97 years
Therefore, it will take approximately 6.97 years for infant mortality to be reduced by 30% in the Senegal program.