Answer and Explanation:
To determine the population by the year 2050 using the given growth equation, we need to substitute the values and solve for the variable. The growth equation given is:
5000 = 1000 + k*t
Here, 5000 represents the population, 1000 represents the initial population at the year 2000, k is the growth rate, and t represents the number of years since 2000.
1. Subtract 1000 from both sides of the equation to isolate the growth term:
5000 - 1000 = k*t
2. Simplify the equation:
4000 = k*t
3. Since we know the time difference between 2000 and 2050 is 50 years, we can substitute t with 50:
4000 = k * 50
4. Divide both sides of the equation by 50 to solve for the growth rate:
4000 / 50 = k
Simplifying further, we get:
80 = k
5. Now that we have the growth rate, we can use the same equation to find the population in 2050:
Population in 2050 = 1000 + k * t
Population in 2050 = 1000 + 80 * 50
Calculating the equation, we get:
Population in 2050 = 1000 + 4000
Population in 2050 = 5000
Therefore, if the population follows the same growth rate as determined by the given equation, the population in the year 2050 would be 5000.