flu exponential

Question

There is a flu outbreak at your school that starts with 10 people. The number of ill students increases by 20% each hour. Write an exponential function to represent the total number of ill students, f(x), where x is the number of hours after the outbreak. How long does it take for at least 100 people to be ill with the flu?

Answer 1

starts with 10, then increases by 20% each hour

20% = 1/5

in 1 hour 10+2 = 12

in 2 hours 12+12/5 = 12+2.4 = 14.4

in x hours f(x) = y=10(1.2)^x

y=100 = 10(1.2)^x

100/10 = 10 = 1.2^x

x = log 10 base 1.2 = ln10/ln1.2 = about 12.62925 hours to reach 100 sick students

= about 12 hours 37 minutes 45.3 seconds