Question

At times t = 1, 2, 3, 4, 5, and 6 seconds, data values yt = 3, 7, 17, 37, 82, and 182 are recorded. a.) Plot the data. (In MATLAB, after storing the t and y values in vectors, use plot(t,y,'o').) From this graph, do you think a linear, exponential, or power function is the best model for the data? b. Produce a semilog plot and use it to roughly estimate the growth rate k for a model of the data given by a curve of the form y = aekt . (In MATLAB, plot(t,log(y),'o') will produce the plot.) c. Produce a log–log plot and use it to roughly estimate the degree n of a power function, for a model of the data of the form y = at n. (In MATLAB, plot(log(t), log(y),'o') will produce the plot.)

Answer 1

From the above plot it looks like an exponential function is the best model for the data.

Exponential model:

y=ae^kt

log(y) = log(a) + kt

if Y=log(y) and A=log(a)

Equation of straight line of above plot:

A=0.3170

a= e^0.3170 = 1.373

And k=0.8145

y=1.373e^0.8145t

Power function model:

y=atⁿ

log(y) = log(a) + nlog(t)

if T=log(t), Y=log(y) and A=log(a)

Equation of straight line of above plot:

Approximate value of n=round(2.6870)=3