Pretend the program in Senegal had been reducing infant mortality at a rate
of 11 % per year. How long would it take for infant mortality
to be reduced by 35 %? How do I go about solving this problem?
when it is reduced by 35%, the remaining not dead is .65 (65%).
.65=1/(1.11)^t solve for t. How? I would use logs.
log of each side.
log.65=-tlog1.11
t= - (log.65/log1.11) Use your calculator to find the right side.
To solve this problem, you can use a formula for exponential growth or decay:
Final Value = Initial Value × (1 + Rate)^Time
In this case, the initial value is 100% (representing the infant mortality rate), and the rate of reduction is 11% per year. You want to find out how many years it takes for the infant mortality rate to be reduced by 35%, so the final value will be 100% - 35% = 65%.
Now, let's plug in the values into the formula:
65% = 100% × (1 - 0.11)^Time
Divide both sides of the equation by 100% to convert percentages into decimals:
0.65 = 1 × (1 - 0.11)^Time
Simplify:
0.65 = 0.89^Time
To solve for Time, take the logarithm of both sides using the base 0.89 (the decay factor):
log base 0.89 (0.65) = Time
Using a calculator or a logarithmic table, you can find the value of Time. Taking the logarithm to the base 0.89 of 0.65 gives you approximately -1.254.
Therefore, it would take approximately -1.254 years for the infant mortality rate to be reduced by 35%. However, this result is not physically meaningful since you cannot have a negative time.
In such cases, it is more appropriate to use the concept of the rule of 70, which estimates the time it takes for a variable to double or halve based on the growth/decay rate. So, dividing 70 by the rate of 11%, we get:
Time = 70 / 11 = 6.36 years
Therefore, it would take approximately 6.36 years for the infant mortality rate to be reduced by 35% if the rate of reduction remains constant at 11% per year.