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3 years ago

Use 2 points to write an equation for each function. Exponential functions.

Mathematics

1 answer:

8_murik_8 [283]3 years ago

6 0

$y=ma^x\\\\(0;\ 10)\to m\cdot a^0=10\to m=10\\\\y=10a^x\\\\(1;\ 20)\to 10a^1=20\ \ \ |:10\\a=2\\\\\boxed{y=20\cdot2^x}\\\\check:\\(-2;\ 2.5)\to2.5=10\cdot2^{-2}\\\\2.5=10\cdot\dfrac{1}{2^2}\\\\2.5=10\cdot\dfrac{1}{4}\\\\2.2=2.2\ correct\ :)\\\\(2;\ 40)\to40=10\cdot2^2\\\\40=10\cdot4\\\\40=40$

Answer: $\boxed{y=10\cdot2^x}$

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What is the limit of the infinite series? ∞∑n=1 (3n^5 / 6n^6 + 1)

hoa [83]

Answer:

The limit of the infinite series is equal to zero.

The nth term test is inconclusive ∵ the limit is equal to 0.

By the Comparison Test, this sum diverges.

General Formulas and Concepts:
Calculus

Limits

Limit Rule [Variable Direct Substitution]: $\displaystyle \lim_{x \to c} x = c$

Series Comparison Tests

nth Term Test
Direct Comparison Test (DCT)

Step-by-step explanation:

Step 1: Define

$\displaystyle \sum^{\infty}_{n = 1} \frac{3n^5}{6n^6 + 1}$

Step 2: Find Convergence

[Series] Define: $\displaystyle a_n = \frac{3n^5}{6n^6 + 1}$
[Series] Set up [nth Term Test]: $\displaystyle \sum^{\infty}_{n = 1} \frac{3n^5}{6n^6 + 1} \rightarrow \lim_{n \to \infty} \frac{3n^5}{6n^6 + 1}$
[nth Term Test] Evaluate limit [Limit Rule - VDS]: $\displaystyle \lim_{n \to \infty} \frac{3n^5}{6n^6 + 1} = 0$
[nth Term Test] Determine Conclusiveness: $\displaystyle 0 ,\ \sum^{\infty}_{n = 1} \frac{3n^5}{6n^6 + 1} \ \text{can't be concluded that it converges}$

Therefore, the nth term test is inconclusive and another test must be done.

Step 3: Find Convergence Pt. 2

[DCT] Condition 1 [Define comparing series]: $\displaystyle \frac{1}{2} \sum^{\infty}_{n = 1} \frac{1}{n}$
[DCT] Condition 1 [Test convergence of comparing series]: $\displaystyle p = 1 ,\ \frac{1}{2} \sum^{\infty}_{n = 1} \frac{1}{n} \ \text{divergent by p-series (harmonic series)}$

∴ since the comparison series is divergent, then our original series is also divergent according to the Direct Comparison Test.

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Learn more about limits: brainly.com/question/26091024

Learn more about Taylor Series: brainly.com/question/23558817

Topic: AP Calculus BC (Calculus I + II)

Unit: Taylor Series

4 0

3 years ago

Read 2 more answers

explain how to use mental if it took marty 42 minutes to write a book and 18 mins correcting his report.

nika2105 [10]

I think the correct answer would be, I did 42 minutes + 18 minutes. So it took Marty 60 minutes to read his book and correct his report.

Hope this helped! ;)

3 0

4 years ago

Find the area of a regular polygon with 100 sides with a perimeter of 100 units

Gnom [1K]

The area of any regular polygon with n sides of length s is

s = 100/100 = 1

Area =~ 795.55 sq units

4 0

3 years ago

BRAINLIEST ASAP! PLEASE HELP ME :)

Afina-wow [57]

Answer:

$\large \boxed{\textbf{30.54 yr}}$

Step-by-step explanation:

For species A,

$P =2000e^{0.05t}$

For species B,

$P =5000e^{0.02t}$

When their populations are equal,

$\begin{array}{rcl}2000e^{0.05t} & = & 5000e^{0.02t}\\e^{0.05t} & = & 2.5e^{0.02t}\\0.05t & = & \ln2.5 + 0.02t\\0.05t & = & 0.9163 + 0.02t\\0.03t & = & 0.9163\\t& = & \dfrac{0.9163}{0.03}\\\\& = & \mathbf{30.54}\\\end{array}\\\text{The populations of species A and B will be the same in $\large \boxed{\textbf{30.54 yr}}$}$

The diagram below shows the population of Species A overtaking that of Species B in about 30.5 yr.

3 0

4 years ago

What would you get if you multiple-2x with x

bezimeni [28]

You would get -2x^2.

4 0

3 years ago