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Ball bearings are hardened through a process of heating and then rapid cooling. The temperature of the ball during this process can be estimated using the equation:

T(t) = (ti-to)*e^(-t/T)+to

where ti = initial ball temp = 800 degrees celcius

to = initial oil temp = 40 degrees celcius

t = time = 0-180 seconds at 1 second intervals

T = time contraint

Create a graph in matlab showing ball temperature versus time. the graph should have 3 curves for the 3 time contraints entered by the user. the 3 time constrains are:

T = 20, 50, and 80 seconds

Use a while loop to generate the arrays to be plotted, with a stopping condition that the value of temperature for all 3 arrays to be plotted is less than 80 degrees celcius. Include a function that is called from the script to get the time constant from the user, and to verify that it is a value between 20 and 100 inclusive. If not, stay in a loop until the user enters a value between 20 and 100.

The final answer should look like this:

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