Question

High SchoolMathematics 5 points A bean plant grows at a constant rate for a month. After 10 days, the plant is 25 centimeters tall. After 20 days, the plant is 45 centimeters tall. Which equation models the height of the plant, y, after x days?

Answer 1

We have a function of the form:

`y = A * b ^ t`
Where,
A: initial height
b: growth rate
We must find the values of A and b.
For this we use the following data:
After 10 days, the plant is 25 centimeters tall:

`25 = A * b ^ {10}`After 20 days, the plant is 45 centimeters tall

`45 = A * b ^ {20}`
We observe that we have a system of equations where there are:
2 equations
2 unknowns
Solving the system we have:

`A = 13.9 b = 1.06`
Thus, substituting values, we have that the equation that models the problem is:

`y = 13.9 * 1.06 ^ t`
Answer:
An equation that models the height of the plant, and, after x days is:

`y = 13.9 * 1.06 ^ t`