Final answer:
The initial value of the growth function for a plant growing linearly is its height when first planted. Given the plant's current height of 28 cm and growth rate of 2 cm/month, the initial value is simply 28 centimeters as it is the height at time zero.
Step-by-step explanation:
The student has asked to determine the initial value of the growth function for a plant that has been growing linearly. Given that the plant is currently 28 centimeters tall and that it has been growing at a rate of 2 centimeters per month, we can infer that the initial value is the height of the plant when it was first planted (at time zero).
To find the initial height, we can use the linear growth formula H(t) = H0 + rt, where H(t) is the height at time t, H0 is the initial height, and r is the growth rate. Since we don't know the number of months that have passed and only the current height and rate, we can simply write the formula as H(t) = 28 cm and r = 2 cm/month. Solving for H0 when t = 0 gives us H0 = 28 cm - (2 cm/month * t).
Since we want the initial value (at t = 0), we see that the term involving time will be zero. Therefore, the initial value is simply the current height, which is 28 centimeters.