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3 years ago

How to tell linear exponential and exponential decay apart

Mathematics

1 answer:

vova2212 [387]3 years ago

5 0

Answer:

Step-by-step explanation:

A typical equation for exponential change looks like this:

y = a(r)^(n),

where a is the initial value, r is the common ratio and n is the number of periods.

To answer your question: If r > 0, you're dealing with exponential growth;

if r < 0, you're dealing with exponential decay.

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The distribution of heights of young women aged 18 to 24 is approximately normal with a mean of 64.5 inches and a standard devia

Lena [83]

The 68 - 95 - 99.7 rule, gives the basis to solve this question.

It says that for a normal distribution 95% of the results are between the mean minus 2 standard deviations and the mean plus 2 standard deviations.

Here:
mean = 64.5 inches,
standard deviaton = 2.5 inches

mean - 2 standard deviations = 64.5 inches - 5 inches = 59.5 inches

mean + 2 standard deviations = 64.5 inches + 5 inches = 69.5 inches

Then, the answer is that 95% of women range approximately between 59.5 inches and 69.5 inches.

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4 years ago

Question 12 please , thank you in advance.

Monica [59]

I thing it might be C

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4 years ago

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I found the interval of convergence, but I am not sure how to do the second part, finding the sum of the series as a function of

antiseptic1488 [7]

The given series is geometric with common ratio $6^x - 9$ , which converges if $|6^x - 9|$ (i.e. the interval of convergence). We have the well-known result

$\displaystyle |r| < 1 \implies \sum_{n=0}^\infty ar^n = \frac{a}{1-r}$

If you're not familiar with that result, it's easy to reproduce.

Let $S_N$ be the $N$ -th partial sum of the infinite series,

$\displaystyle S_N = \sum_{n=0}^N \left(6^x - 9\right)^n = 1 + \left(6^x - 9\right) + \left(6^x - 9\right)^2 + \cdots + \left(6^x - 9\right)^N$

Multiply both sides by the ratio.

$\left(6^x - 9\right) S_N = \left(6^x - 9\right) + \left(6^x - 9\right)^2 + \left(6^x - 9\right)^3 + \cdots + \left(6^x - 9\right)^{N+1}$

Subtract this from $S_N$ to eliminate all the powers of the ratio between 0 and $N+1$ .

$\left(1 - \left(6^x - 9\right)\right) S_N = 1 - \left(6^x - 9\right)^{N+1}$

Solve for $S_N$ .

$S_N = \dfrac{1 - \left(6^x - 9\right)^{N+1}}{10-6^x}$

Now as $N\to\infty$ , the exponential term converges to 0 and we're left with

$\displaystyle \sum_{n=0}^\infty \left(6^x-9\right)^n = \lim_{N\to\infty} S_N = \boxed{\frac1{10-6^x}}$

7 0

2 years ago

Can someone please help me find the area and perimeter of this shape? Thank you!

mojhsa [17]

Answer:

136

Step-by-step explanation:

The area of the triangle is 24 the area of the rectangle is 112

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4 years ago

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I NEED HELP I WILL GIVE ALL POINTS AND MARK BRAINIEST PLEASE HELP ME

ratelena [41]

So a line is 180 degrees. These angles would equal 180. So 180= w + (3w -28). You add 28 too 180, getting 208. Then divide by the 4w. Leading you to w= 52. Plug into the equations to make sure everything checks out

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3 years ago