g 1) The rate of growth of a certain type of plant is described by a logistic differential equation. Botanists have estimated the maximum theoretical height of such plants to be 30 in. At the beginning of an experiment, the height of a plant was 5 in. a) Find an expression for the height of the plant after t days. (To find k, suppose the plant grew to 12 in. after 20 days.) b) What was the height of the plant after 30 days

a) The expression for the height, 'H', of the plant after 't' day is;

b) The height of the plant after 30 days is approximately 19.426 inches

Step-by-step explanation:

The given maximum theoretical height of the plant = 30 in.

The height of the plant at the beginning of the experiment = 5 in.

a) The logistic differential equation can be written as follows;

Using the solution for the logistic differential equation, we get;

Where;

A = The condition of height at the beginning of the experiment

M = The maximum height = 30 in.

Therefore, we get;

A = 5

When t = 20, H = 12

We get;

∴ -(30·k)·20 = ㏑(1.5)

k = ㏑(1.5)/(30 × 20) ≈ 6·7577518 × 10⁻⁴

k ≈ 6·7577518 × 10⁻⁴

Therefore, the expression for the height, 'H', of the plant after 't' day is given as follows

b) The height of the plant after 30 days is given as follows

At t = 30, we have;

The height of the plant after 30 days, H ≈ 19.426 in.

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step-by-step explanation: