Finding exponential function relating number of cases and days of month

Question

the number of flu cases on May 1 were 3 and on may 9 were 19. If he growth is exponential find the function that relates t (day of month) to N ( number of cases). How many cases on May 21

Answer 1

To construct the function without a graphing calculator, the function has the form N = A(B)^t.

 

Since (1, 3) is on the graph, 3 = A(B)¹.  So, A = 3/B

 

Since (9, 19) is on the graph, 19 = A(B)⁹ .

 

Replace A by 3/B:  19 = (3/B)(B)⁹

 

                                  19 = 3(B)⁸

 

B⁸ = 6.33333333

 

B = (6.3333333)^1/8  = 1.2595

 

So, A = 3/B = 2.38186

 

Equation:  N = 2.38186(1.2595)^t

Answer 2

Your coordinate point will be in the form (t, N)

 

where t = day of month may

 

Point 1 = (1, 3)

Point 2 = (9, 19)

 

Use your graphing calculator to find the exponential model.  Go to STAT and EDIT, then press ENTER.  You will see a chart.  In the first column of the chart enter the x-coordinates.  In the second column, enter the y-coordinates.  Once you complete that step, go to STAT, and go CALC. Press ENTER. Scroll down the list until you see ExpReg.  Press ENTER twice.  You will have your function.

 

y = 2.382(1.260)^t