Question

Numerically approximate the solution to the differential equation

(dB)/(dt)=0.04B
with initial value B=900 when t=0.
Compute each value using linear approximation (this method is also called Euler's method).
A. Delta t=1 and 1 step: B(1)~~
B. Delta t=0.5 and 2 steps: B(1)~~
C. Delta t=0.25 and 4 steps: B(1)~~
Remark: on an exam, you may be asked to do a few simple iterations of Euler's method by hand, and you may also be asked about using a spreadsheet, so make sure you know how to do it both ways. For this question, Euler's Method leads to a nice pattern. If you simplify every step, you may find an easy way to do it by hand.

Answer 1

Euler's method is a numerical approximation method used to solve differential equations. When using Euler's method with different time intervals, we can approximate the value of B(1) for the given differential equation.

Step-by-step explanation:

Euler's method is a numerical approximation method used to solve differential equations. To use Euler's method, we start with the initial value of the function, in this case, B(0) = 900. Then, we use the derivative of the function, dB/dt = 0.04B, to approximate the change in the function over a small time interval.

Finally, we update the value of the function using the formula B(1) = B(0) + delta t * dB/dt, where delta t is the time interval.

1. For delta t = 1 and 1 step, B(1) is approximately 936.
2. For delta t = 0.5 and 2 steps, B(1) is approximately 949.44.
3. For delta t = 0.25 and 4 steps, B(1) is approximately 955.93.