Exponential growth question?

Question

https://gyazo.com/c16efc1b05e028fcb402edeefa7f1738

 

The answers in the photo are the correct answers, but I just don't know how to go about solving the problem. Any help would be appreciated!

Answer 1

Denise,

 

You are given a formula for the percent infected after t days:

 

V(t) = 100 / (1 + 99e^-0.175t)

 

Part (A)

 

To find the percent infected after 12 days, just substitute t = 12 in the equation and simplify: 

 

V(t) = 100 / (1 + 99e^-0.175*12) = 7.62

 

7.62% are infected after 12 days

 

Part (B)

 

To find the number of days it takes for 90% to get infected, set 90 = V(t) and solve for t.

 

90 = 100 / (1 + 99e^-0.175t)

 

Now do some algebra to find t:

 

1 + 99e^-0.175t = 100/90 = 1.111

 

99e^-0.175t = 1.111 - 1 = 0.111

 

e^-0.175t = 0.111 / 99 = 1.121 x 10^-3

 

-0.175t = ln(1.121 x 10^-3) = -6.794 

 

t = -6.794 / (-0.175) = 38.82 days

 

The web page says 38.81 days, which is a slight difference in roundoff.  The important thing is that you understand the math involved.