In 1993, the moose population in a park was measured to be 3450 . By 1996, the population was measured again to be 3960 . If the population continues to change linearly: Find a formula for the moose population, \( P \), in terms of \( t \), the years since 1990 . \( P(t)= \) What does your model predict the moose population to be in 2004? W

To find a formula for the moose population \( P \) in terms of \( t \), we first note that in 1993 (which corresponds to \( t = 3 \)), the population was 3450, and in 1996 (\( t = 6 \)), it was 3960. We can find the slope \( m \) of the line representing the population growth: \[ m = \frac{P(6) - P(3)}{6 - 3} = \frac{3960 - 3450}{3} = \frac{510}{3} = 170 \] Now that we have the slope, we can use the point-slope form of a linear equation. Using the point (3, 3450), we can write: \[ P(t) = 170(t - 3) + 3450 \] Expanding this gives us: \[ P(t) = 170t - 510 + 3450 = 170t + 2940 \] So the formula for the moose population in terms of \( t \) is: \[ P(t) = 170t + 2940 \] To predict the moose population in 2004, we find \( t = 14 \) (since 2004 - 1990 = 14): \[ P(14) = 170(14) + 2940 = 2380 + 2940 = 5320 \] Thus, the model predicts the moose population to be 5320 in 2004.