Question

In 1992, the moose population in a park was measured to be 4660. By 1998, the population was measured again to be 5560. If the population continues to change linearly:

A.) Find a formula for the moose population, P, in terms of, t, the years since 1990.
P(t)=
B.) What does your model predict the moose population to be in 2007?

Answer 1

The formula for the moose population, P, in terms of years since 1990 is P(t) = 4660 + 150 * (t - 1990). Using this formula, the moose population in 2007 would be predicted to be -290,510, which is not a realistic result.

Step-by-step explanation:

To find a formula for the moose population, P, in terms of years since 1990, we can use the formula for a linear equation. Let's call the year since 1990 't'.

A.) Finding a formula for the moose population:

Step 1: Determine the change in population and the change in years. In 1992, the population was 4660, and in 1998, the population was 5560. This means the population increased by 900 over 6 years.

Step 2: Find the rate of change in population per year. Divide the change in population (900) by the change in years (6) to get a rate of change of 150 per year.

Step 3: Write the formula using the rate of change and the initial population. The formula is:

P(t) = P(1990) + (rate of change) * t

Since we start measuring in 1990, the initial population is 4660. Substituting the values, we get:

P(t) = 4660 + 150 * (t - 1990)

B.) Predicting the moose population in 2007:

To predict the population in 2007, we need to find the value of t for that year. Since 2007 is 17 years after 1990, t = 17. Substituting this value into the formula, we get:

P(2007) = 4660 + 150 * (17 - 1990) = 4660 + 150 * (-1973) = -290,510.

However, a negative population is not realistic, so we can conclude that our linear model does not accurately predict the population in 2007.