Cicero has a population of 6200 people and is growing at a rate of 8% per year . Mattydale has a population of 8750 and is growing at a rate of 6% per year create and equation solve the problem and in how many years to the nearest year will Cicero have a greater population than mattydale
6200 * 1.08^t = 8750 * 1.06^t
(1.08/1.06)^t = 8750/6200
...
To solve this problem, we can set up an equation to compare the population growth of Cicero and Mattydale over time.
Let's assume "x" represents the number of years.
The equation for Cicero's population growth would be:
Cicero_population = 6200 * (1 + 0.08)^x
The equation for Mattydale's population growth would be:
Mattydale_population = 8750 * (1 + 0.06)^x
Now, to find out how many years it takes for Cicero to have a greater population than Mattydale, we need to solve the equation:
6200 * (1.08)^x = 8750 * (1.06)^x
To solve this equation, we can use logarithms. Taking the logarithm (base doesn't matter) of both sides of the equation, we get:
log(6200) + x * log(1.08) = log(8750) + x * log(1.06)
Now, we can isolate the variable x:
x * log(1.08) - x * log(1.06) = log(8750) - log(6200)
x * (log(1.08) - log(1.06)) = log(8750) - log(6200)
x = (log(8750) - log(6200)) / (log(1.08) - log(1.06))
Using a calculator to evaluate the right side of the equation, we find that x ≈ 26.89. However, since we are looking for a whole number of years, we round this value to the nearest year.
Therefore, it would take approximately 27 years for Cicero to have a greater population than Mattydale.