Question

35 50 77 91 98 49 Day Heightin.85 21 21 63 89 The data can be modeled with a function in the for where y is the height, H is a maximum height, a and b are constants, and r is the number of days. By assuming that H - 102 in., determine the constants a and b such that the function best fits the data. Use the function to estimate the height in day 40. In one figure, plot the function and the data points.

Answer 1

log(11-y) =-bt-a comparing,Y = MX + C

Code:

clc
clear

t = [7 21 35 49 63 77 91];
y = [8.5 21 50 77 89 98 99];
H = 102;

% Fitting linear model
Y = log((H - y)./y);
X = t;

YP = polyfit(X, Y, 1);
b = -YP(1)
a = -YP(2)

xq = 40;
yq = H./(1 + exp(-a - b*40));
disp("Height(in.) at t = 40 is "+num2str(yq));
yy = H./(1 + exp(-a - b.*t));
plot(t, y, 'ro', t, yy, '-b')
legend('data', 'function');

Output:

120 O data function 100 80 60 o/ 40 20 0 0 10 20 304050 60 70 80 90100

b- 0.073325 -2.7419 Height (in.) at t 40 is 55.8568