00:01
So the number of individuals infected is modeled by the function n at time t is 9500 t minus 2000 divided by 4 plus t where t is time in months.
00:16
So t is the number of months.
00:19
And then in part a we're asked to find the number of infected people by the end of the fourth month.
00:25
Well that is n evaluated at 4.
00:28
So that is 9500 times 4 minus 2000 divided by 4 plus 4 is 8.
00:38
And this is equal to 4500.
00:43
And in part b we have to find after how many months there are 5500 infected people.
00:51
Well we said 5500 equal to 9500 times t minus 2000 divided by 4 plus t and solve for t.
01:10
So then we get let's see here 5500 times 4 plus t is equal to 9500 t minus 2000.
01:27
And then that gives us 5500 times 4 is 22000.
01:38
So 22000 plus 5500 t is equal to 9500 t minus 2000.
01:54
And then that gives us subtracting 2000 from both sides is 20 ,000.
02:01
Subtracting 5500 t from both sides we get 20 ,000 is equal to 4000 t.
02:11
And then 20 ,000 divided by 4000 is equal to 5...