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marissa [1.9K]
2 years ago
7

Find the equation of the exponential function represented by the table below:

Mathematics
1 answer:
Leona [35]2 years ago
5 0

Answer:

The exponential equation is;

y = 0.1•0.5^x

Step-by-step explanation:

Here, we want to get the exponential function represented by the table

Mathematically, the general form of an exponential function is;

y = a•b^x

By getting a and b, we have the exponential function

We can use any of the points;

Let us start with (0,0.1)

0.1 = a•b^0

anything raised to zero is 1

0.1 = a * 1

a = 0.1

Now, we have a

Let us work with the second point to get b

The point is (1,0.05)

0.05 = 0.1•b^1

0.05 = 0.1b

b = 0.05/0.1

b = 0.5

Thus, we have the equation as;

y = 0.1•0.5^x

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KengaRu [80]

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3 years ago
Find two solutions to the equation (x^3 − 64)(x^5 − 1) = 0.
Rashid [163]

Answer:

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Step-by-step explanation:

Data provided in the question:

(x³ − 64) (x⁵ − 1) = 0.

Now,

for the above relation to be true the  following condition must be followed:

Either  (x³ − 64) = 0 ............(1)

or

(x⁵ − 1) = 0 ..........(2)

Therefore,

considering the first equation, we have

(x³ − 64) = 0

adding 64 both sides, we get

x³ − 64 + 64 = 0 + 64

or

x³ = 64

taking the cube root both the sides, we have

∛x³ = ∛64

or

x = ∛(4 × 4 × 4)

or

x = 4

similarly considering the equation (2) , we have

(x⁵ − 1) = 0

adding the number 1 both the sides, we get

x⁵ − 1 + 1 = 0 + 1

or

x⁵ = 1

taking the fifth root both the sides, we get

\sqrt[5]{x^5}=\sqrt[5]{1}

also,

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therefore,

\sqrt[5]{x^5}=\sqrt[5]{1^5}

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4 0
3 years ago
Suppose that a study of elementary school students reports that the mean age at which children begin reading is 5.9 years with a
Bas_tet [7]

Answer:

5.9 years.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \mu = p and standard deviation s = \sqrt{\frac{p(1-p)}{n}}

In this question:

Mean of the population is \mu = 5.9

If a sampling distribution is created using samples of the ages at which 69 children begin reading, what would be the mean of the sampling distribution of sample means?

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3 0
2 years ago
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leva [86]

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Step-by-step explanation:

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