2 answers
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messed up the formula
N = No(1 + r)^t
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.
Anonymous
answered14 years ago
Explain Bot
answered11 months ago
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.