Two different species of deer are housed in two separate areas of a wildlife park. The initial population of species A was 300, and the population is increasing by 15% every year. The initial population of species B was 400, and the population is increasing by 7% every year.Use the given information to determine when the two species will have the same population.After years, the populations of the two species will be approximately equal, with deer of each species.
Question
Two different species of deer are housed in two separate areas of a wildlife park. The initial population of species A was 300, and the population is increasing by 15% every year. The initial population of species B was 400, and the population is increasing by 7% every year.Use the given information to determine when the two species will have the same population.After years, the populations of the two species will be approximately equal, with deer of each species.
Solution
To solve this problem, we need to set up two equations that represent the population growth of each species of deer over time.
For species A, the population growth can be represented by the equation:
A = 300 * (1 + 0.15)^t
For species B, the population growth can be represented by the equation:
B = 400 * (1 + 0.07)^t
We want to find out when the populations will be equal, so we set the two equations equal to each other and solve for t:
300 * (1 + 0.15)^t = 400 * (1 + 0.07)^t
To solve this equation for t, we can use a method called logarithms. First, divide both sides by 300:
(1 + 0.15)^t = 400/300 * (1 + 0.07)^t
Then, take the natural log (ln) of both sides:
t * ln(1 + 0.15) = ln(400/300) + t * ln(1 + 0.07)
Solve for t:
t = ln(400/300) / (ln(1 + 0.15) - ln(1 + 0.07))
Plug the values into a calculator to get the approximate value of t. This will give you the number of years it will take for the populations of the two species to be approximately equal.
Similar Questions
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