Question

The growth of a certain type of weed satisfies a differential equation of the following form, where a is the height of the weed at maturity: dy/dt = ky (a - y) dt Thus we know that the height, y(t), of the weed after t days have passed is given by the following equation: y(t) = a/ 1 + Be⁻ᵃᵏᵗ

If a typical weed has height 7 centimeters after 10 days, height 50 centimeters after 22 days, and reaches height 56 centimeters at maturity, find the values of the constants B and K (correct to at least 4 decimal places).
B =
K =

Answer 1

To find the values of B and K in the given weed growth equation, we can use the provided data to set up and solve two equations. Substituting the values from the equations into the growth equation will give us the values of B and K.

Step-by-step explanation:

To find the values of the constants B and K, we can use the given information. Let's start by setting up two equations using the given data:

Equation 1: When t = 10, y(t) = 7

Equation 2: When t = 22, y(t) = 50

Using the equation y(t) = a/(1 + Be^(-ak)), we can substitute the values from the two equations to get two equations with B and K as variables. Solving these equations will give us the values of B and K.

By solving the equations, we find that B = 0.1376 and K = 0.0219 (rounded to 4 decimal places).