You can find the size of a population after t years using the formula N = No(1 + r)t where No is the initial size of the population, N is the final size of the population, r is the rate of growth or decay per time period, and t is the number of time periods.
Just over 1 million prisoners (actually 1,080,000) were in the United States in 1995. Assume that the growth rate, r, is the same for the general population at 76% per 15 years. In which year would you expect the number of prisoners to double?
Don't know how to set this up to solve.
messed up the formula
N = No(1 + r)^t
To find the year in which the number of prisoners is expected to double, we need to use the given formula N = No(1 + r)t.
First, let's identify the given information:
No (initial size of the population) = 1,080,000
r (rate of growth or decay) = 76% per 15 years
t (number of time periods) = unknown (we need to find this)
Next, we need to find the value of N (final size of the population) when it doubles. Since we are looking for the year when the number of prisoners doubles, N will be twice the initial number of prisoners, which is 2 * 1,080,000 = 2,160,000.
Now we can plug in the known values into the formula and solve for t:
2,160,000 = 1,080,000(1 + 0.76/15)t
To simplify the equation, divide both sides by 1,080,000:
2 = (1 + 0.76/15)t
Next, subtract 1 from both sides of the equation:
1 = 0.76/15)t
Now, isolate t by dividing both sides by 0.76/15:
t = 15 * (1 / 0.76)
Calculating the value of t, we have:
t ≈ 19.7368
The value of t represents the number of 15-year periods. Since we are looking for the year, we need to multiply t by 15 (the length of each time period) to get the total number of years:
t (in years) ≈ 19.7368 * 15
Calculating this value, we have:
t (in years) ≈ 296.052
Rounding this to the nearest year, we get:
t ≈ 296
Therefore, we would expect the number of prisoners to double around the year 1995 + 296 = 2291.
However, please note that this calculation assumes a constant growth rate, which might not accurately represent the actual population growth of prisoners. Additionally, external factors and policies may affect the growth rate over time.