Answer:
C. 
General Formulas and Concepts:
<u>Calculus</u>
- Mean Value Theorem (MVT) - If f is continuous on interval [a, b], then there is a c∈[a, b] such that
- MVT is also Average Value
Step-by-step explanation:
<u>Step 1: Define</u>
f'(c) = 20
Interval [1, b]
<u>Step 2: Check/Identify</u>
Function [1, b] is continuous.
Derivative [1, b] is continuous.
∴ There exists a c∈[1, b] such that
<u>Step 3: Mean Value Theorem</u>
- Substitute:
- Rewrite:
And we have our final answer!
The answer is rounded to the nearest tenth.
Answer:
- 5 min: 3,029,058
- 10 min: 3,398,220
- 60 min: 10,732,234
Step-by-step explanation:
The given function is evaluated by substituting the given values of t. This requires using the exponential function of your calculator with a base of 'e'. Many calculators have that value built in, or have an e^x function (often associated with the Ln function).
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<h3>5 minutes</h3>
The number of bacteria present after 5 minutes is about ...
f(5) = 2.7×10^6×e^(0.023×5) ≈ 3,029,058
<h3>10 minutes</h3>
The number of bacteria present after 10 minutes is about ...
f(10) = 2.7×10^6×e^(0.023×10) ≈ 3,398,220
<h3>60 minutes</h3>
The number of bacteria present after 60 minutes is about ...
f(60) = 2.7×10^6×e^(0.023×60) ≈ 10,732,234
50 would be a good choice of answer
