The model N = 10(4+3t)/1.25 describes the number of deer (N) in a park t years after 40 deer are introduced into the region. Approximately how long will it take the deer population to reach 224?
How would I set up this equation?
put in 224 for N, and solve for t.
To set up the equation, you need to equate the given model to the desired population size and solve for the value of t.
Given: N = 10(4+3t)/1.25
Desired population size: N = 224
Setting up the equation:
224 = 10(4+3t)/1.25
To solve for t, you need to isolate the variable t. Here's the step-by-step process:
1. Multiply both sides of the equation by 1.25 to get rid of the denominator:
224 * 1.25 = 10(4+3t)
2. Simplify the equation on the right side:
280 = 40 + 30t
3. Subtract 40 from both sides to isolate 30t:
280 - 40 = 40 - 40 + 30t
240 = 30t
4. Divide both sides of the equation by 30 to solve for t:
240/30 = 30t/30
8 = t
Therefore, approximately after 8 years, the deer population will reach 224.