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1 year ago

Tell whether the function represents exponential growth or exponential decay.f (x) = 3 (3)

Mathematics

1 answer:

guapka [62]1 year ago

8 0

We can write an exponential function as:

$f(x)=a\cdot b^x$

The value that determines if it corresponds to growth or decay is the coefficient "b": if b is less than 1, the function represents an exponential decay, and if it is bigger than 1 it represents an exponential gorwth.

In this case, f(x) = 3 * (3/4)^x, the value of b is b=3/4 and it is less than 1, so it represents an exponential decay:

Answer: Exponential decay

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A leprechaun places a magic penny under a girls pillow. The next night there are 2 magic pennies under her pillow. The following

kiruha [24]

Answer:

After 47 days she will have more than 90 trillion pennies.

Step-by-step explanation:

At the beginning there was 1 penny. At the second day the amount of pennies under the pillow became 2.

The amount of pennies doubled each day. So the series is,

$1,2,4,8,16,32,.....$

This series is in geometric progression.

As the pennies from each of the previous days are not being stored away until more pennies magically appear so the sum of series will be,

$S_n=\dfrac{a(r^n-1)}{r-1}$

where,

a = initial term = 1,

r = common ratio = 2,

As we have find the number of days that would elapse before she has a total of more than 90 trillion, so

$\Rightarrow 90\times 10^{12}\le \dfrac{1(2^n-1)}{2-1}$

$\Rightarrow 90\times 10^{12}\le \dfrac{2^n-1}{1}$

$\Rightarrow 90\times 10^{12}\le 2^n-1$

$\Rightarrow 2^n\ge 90\times 10^{12}+1$

$\Rightarrow \log 2^n\ge \log (90\times 10^{12}+1)$

$\Rightarrow n\times \log 2\ge \log (90\times 10^{12}+1)$

$\Rightarrow n \ge \dfrac{\log (90\times 10^{12}+1)}{\log 2}$

$\Rightarrow n \ge 46.4$

$\Rightarrow n\approx 47$

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3 years ago

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Phantasy [73]

Step-by-step explanation

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3 years ago

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3x - 9 + 4x Please Help

Wewaii [24]

Answer:

Add like terms 7x - 9

Step-by-step explanation:

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3 years ago

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For the following hypothesis test, determine the null and alternative hypotheses. Also, classify the hypothesis test as two-tail

bagirrra123 [75]

Answer:

Option B:

$H_0: \mu = 22.1$

$H_a: \mu \neq 22.1$

Classification:

The hypothesis test is Two-tailed.

Step-by-step explanation:

The mean length of imprisonment for motor-vehicle theft offenders in this country is 22.1 months.

This means that the null hypothesis is that the mean is of 22.1 months, that is:

$H_0: \mu = 22.1$

A hypothesis test is to be performed to determine whether the mean length of imprisonment for motor-vehicle theft offenders in this city differs from the national mean of 22.1 months.

At the alternate hypothesis, we test if this mean is different of 22.1, that is:

$H_a: \mu \neq 22.1$

Which means that the answer is given by option b).

Which of the following is the correct classification of the hypothesis test?

We test if the mean is different from a value, which means that the hypothesis test is Two-tailed.

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3 years ago

Find the length of x. A:48 B:100 C:64 D: 2304 (PLEASE HELP!!!)

Furkat [3]

Answer:

Step-by-step explanation:

That the answer Plss follow me thanks

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