The temperature inside a sauna is rising 4° per hour is the temperature inside the sauna continuous or discrete data.
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<h3>There are 189 bacteria in 5 hours</h3><h3>There are 13382588 bacteria in 1 day</h3><h3>There are 
bacteria in 1 week</h3>
<em><u>Solution:</u></em>
Given that,
A type of bacteria has a very high exponential growth rate of 80% every hour
There are 10 bacteria
<em><u>The increasing function is given as:</u></em>
Where,
y is future value
a is initial value
r is growth rate
t is time period
From given,
a = 10
<em><u>Determine how many will be in 5 hours</u></em>
Substitute t = 5
y = 189
Thus, there are 189 bacteria in 5 hours
<em><u>Determine how many will be in 1 day ?</u></em>
1 day = 24 hours
Substitute t = 24
Thus, there are 13382588 bacteria in 1 day
<em><u>Determine how many will be in 1 week</u></em>
1 week = 168
Substitute t = 168
Thus there are bacteria in 1 week
The smallest positive integer that the intermediate value theorem guarantees a zero exists between 0 and a is 3.
What is the intermediate value theorem?
Intermediate value theorem is theorem about all possible y-value in between two known y-value.
x-intercepts
-x^2 + x + 2 = 0
x^2 - x - 2 = 0
(x + 1)(x - 2) = 0
x = -1, x = 2
y intercepts
f(0) = -x^2 + x + 2
f(0) = -0^2 + 0 + 2
f(0) = 2
(Graph attached)
From the graph we know the smallest positive integer value that the intermediate value theorem guarantees a zero exists between 0 and a is 3
For proof, the zero exists when x = 2 and f(3) = -4 < 0 and f(0) = 2 > 0.
<em>Your question is not complete, but most probably your full questions was</em>
<em>Given the polynomial f(x)=− x 2 +x+2 , what is the smallest positive integer a such that the Intermediate Value Theorem guarantees a zero exists between 0 and a ?</em>
Thus, the smallest positive integer that the intermediate value theorem guarantees a zero exists between 0 and a is 3.
Learn more about intermediate value theorem here:
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