Question

the ebola virus has an infection rate of 11% per day as compared to the SARS virus, which has a rate of 4% per day. If there were one case of Ebola and 30 cases of SARS initially reported to the authorities and cases are reported each day, which statement is true?​

Answer 1

3) At day 10 there are more SARS cases, but at day 53 there are more Ebola cases.

Explanation:

First let's get our variables.

Ebola Rate = 11% or 0.11

SARS Rate = 4% or 0.04

x = number of days

Let Ebola = e(x)

Let SARS = s(x)

So the total number of cases are:

e(x) =
`1(1.11)^(x)`

s(x) =
`30(1.04)^(x)`

At day 10:

e(10) =
`1(1.11)^(10)`

e(10) =
`1(2.84)`

e(10) =
`2.84`

s(10) =
`30(1.04)^(10)`

s(10) =
`30(1.48)`

s(10) =
`44.41`

So at day 10 the number of cases of Ebola will be 2 and SARS at 44.

At day 53:

e(53) =
`1(1.11)^(53)`

e(53) =
`1(252.42)`

e(53) =
`252.42`

s(53) =
`30(1.04)^(53)`

s(53) =
`30(7.99)`

s(53) =
`239.82`

By day 53, Ebola will overtake SARS at 252 cases to 239 cases.