Question 1194378
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a = initial number of people infected = 71
r = 0.12 = growth rate in decimal form
b = 1 + r = 1+0.12 = 1.12 = growth factor


The template
y = a*b^x
becomes
y = 71*(1.12)^x
and this is an exponential model for the number who fall ill


x = number of days
y = number who are ill


The town has a population of 2621
95% of which is 0.95*2621 = 2489.95 which I'll round to the nearest whole number to get 2490


Once the town has 2490 ill people, it will reach an infection rate of about 95%.


Replace y with 2490 and solve for x.
You'll need logarithms to isolate the exponent.


y = 71*(1.12)^x
2490 = 71*(1.12)^x
2490/71 = (1.12)^x
(1.12)^x = 2490/71
(1.12)^x = 35.070423
Log[ (1.12)^x ] = Log[ 35.070423 ]
x*Log[ 1.12 ] = Log[ 35.070423 ]
x = Log[ 35.070423 ]/Log[ 1.12 ]
x = 31.389741


Let's check to see what happens when we plug in x = 31
y = 71*(1.12)^x
y = 71*(1.12)^31
y = 2382.413007
y = 2382
We don't reach the goal of 2490, but we get pretty close.


Now try x = 32
y = 71*(1.12)^x
y = 71*(1.12)^32
y = 2668.302568
y = 2668
We're now over the hurdle of 2490


Answer: <font color=red>Day 32</font>
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