The height of a plant, in centimeters, t months after being planted is modeled by h(t) = 2.5t + 8. What does the value 8 represent in this…

In the model $h(t) = 2.5t + 8$, the constant term is the value when $t = 0$, since $h(0) = 2.5(0) + 8 = 8$. At $t = 0$ the plant has just been planted, so 8 is the plant's height in centimeters at planting, choice C. Choice A describes 2.5, the slope, which is the monthly growth rate. Choice B confuses the output and the input: the height after 8 months would be $h(8) = 28$ centimeters. Choice D has no basis in the model; doubling would happen when $2.5t + 8 = 16$, at $t = 3.2$ months. The intercept is the starting amount.