Linear Growth And Decay

Suppose a plant has an initial height of $1.75$ feet and it grows by a constant amount each month. We want to find the height after $7$ months if the growth rate is $0.5$ feet per month, and then write the linear growth function.

First, identify the initial value (y-intercept) and the rate of change (slope). The plant grows at a constant rate, meaning we add feet for every month that passes.

To find the specific height after $7$ months, multiply the rate by the number of months and add the initial height: $1.75 + (7 \times 0.5) =$ feet.

We can generalize this pattern as a linear relationship since the quantity increases by a fixed amount over equal intervals. The mathematical function relating height $h$ and time $t$ in months is $h = 1.75 +$ $t$.