Differential Equations? Fill in the table.

[ani9890]

Fill in the missing values in the table given if you know that dy/dt=0.2y. Assume the rate of growth given by dy/dt is approximately constant over each unit time interval and that the initial value of y is 6.

Table:
t-0-1-2-3-4
y-6-?-?-?-?
(fill in the missing values where there is a question mark)

I got:
t = 1, y = 7.33
At t = 2 , y = 8.95
At t = 3 , y =10.93
At t = 4 , y = 13.35
using y=6e^(.2t)

but it is wrong, Help?

 

[LCKurtz]

Fill in the missing values in the table given if you know that dy/dt=0.2y. Assume the rate of growth given by dy/dt is approximately constant over each unit time interval and that the initial value of y is 6.

Table:
t-0-1-2-3-4
y-6-?-?-?-?
(fill in the missing values where there is a question mark)

I got:
t = 1, y = 7.33
At t = 2 , y = 8.95
At t = 3 , y =10.93
At t = 4 , y = 13.35
using y=6e^(.2t)

but it is wrong, Help?

You have apparently just plugged the t values into the exact solution. But that is not what the problem asks you to do. What you are asked to do looks a lot like Euler's approximation method. So start with knowing at t=0 the slope is ##.2(6)##, assume that constant slope to get the value at ##t=1##. Then do the same thing for the next steps.

 

[ani9890]

Thank you, I redid the problem using y₂ = y₁ + m(x₂ - x₁) and got:

t --- y
0 .. 6
1 .. 7.2
2 .. 8.64
3 .. 10.368
4 .. 12.4416

can you please check if this is correct?
Thank you