In 1993, the moose population in a park was measured to be 3800. By 1999, the population was measured again to be 5240 If the population continues to change linearly: Find a formula for the moose population, P,in terms of t,the years since 1990. P(t)=square What does your model predict the moose population to be in 2006? square

## Step 1The problem involves a linear function, which can be represented in the form , where is the slope of the line and is the y-intercept.## Step 2In this case, the slope is the rate of change of the moose population per year, and the y-intercept is the population at the start year (1990).## Step 3We are given two points (3, 3800) and (9, 5240), which represent the population of moose in 1993 and 1999 respectively. We can use these points to calculate the slope .### ** **## Step 4The y-intercept is the population at the start year (1990), which is 1990 - 3 = 1987. So, .## Step 5Therefore, the formula for the moose population in terms of , the years since 1990, is \(P(t) = 220t + 3140\).## Step 6To predict the moose population in 2006, we substitute (since 2006 is 16 years after 1990) into the formula.### **\(P(16) = 220*16 + 3140 = 6760\)**