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Aliun [14]
3 years ago
15

John was born in January. On the first July 4th of his life, his aunt gives him $50 to save for his college education. On every

subsequent July 4th, she gives him $25 dollars more than the previous year. What will John's aunt give him on his 18th July 4th?
$500


A 500$

B$475

C
$425

D
$450
Mathematics
1 answer:
m_a_m_a [10]3 years ago
4 0

Answer:

D. 450

Step-by-step explanation:

You multiply 25*18

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Ap calc multiple choice question; attached below<br> please explain how, please!
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Answer:

C. \frac{f(b)-f(1)}{b-1}=20

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  f'(c)=\frac{f(b)-f(a)}{b-a}
  • MVT is also Average Value

Step-by-step explanation:

<u>Step 1: Define</u>

f(x)=e^{2x}

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 f'(c)=\frac{f(b)-f(a)}{b-a}

<u>Step 3: Mean Value Theorem</u>

  1. Substitute:                    20=\frac{ f(b)-f(1)}{b-1}
  2. Rewrite:                        \frac{ f(b)-f(1)}{b-1}=20

And we have our final answer!

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