(a) A can of soda at temperature (Ti) 25◦ C is placed in a refrigerator, where the
ambient temperature F is 10◦ C. We want to determine how the temperature of
the soda changes over a period of time t from 0 to 100 minutes. A standard way of approaching this type of problem is to subdivide the time interval into a
number of small steps, each of duration dt. If Ti is the temperature at the
beginning of step i, the following model can be used to determine Ti+1:
Ti+1 = Ti + K dt (F − Ti)

where K is the conduction coefficient, a parameter that depends on the
insulating properties of the can and the thermal properties of the soda.
Assume that units are chosen so that time is in minutes and that an interval dt
= 1 minute provides sufficient accuracy. Write a MATLAB script to compute,
display, and plot this update process for K = 0.05.

(b) Write a MATLAB program to compute the sum of the first 15 terms in the
series
5𝑘2 − 2𝑘, where k is from 1 to 15