We have a function of the form:
[tex]y = A * b ^ t
[/tex]
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:
[tex]25 = A * b ^ {10}
[/tex]After 20 days, the plant is 45 centimeters tall
[tex]45 = A * b ^ {20} [/tex]
We observe that we have a system of equations where there are:
2 equations
2 unknowns
Solving the system we have:
[tex]A = 13.9
b = 1.06[/tex]
Thus, substituting values, we have that the equation that models the problem is:
[tex]y = 13.9 * 1.06 ^ t
[/tex]
Answer:
An equation that models the height of the plant, and, after x days is:
[tex]y = 13.9 * 1.06 ^ t
[/tex]
