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Vilka [71]
3 years ago
11

Consider the exponential function f(x)itsgraph.​

Mathematics
1 answer:
dedylja [7]3 years ago
6 0

Answer:

# The growth value of the function is 1/3 ⇒ 2nd

# f(x) shows exponential decay ⇒ 3rd

# The function is a stretched of the function f(x)=(\frac{1}{3}) ^{x} ⇒ 4th

Step-by-step explanation:

* Lets explain the exponential function

- The form of the exponential function is f(x) = a b^x, where a ≠ 0,

  b > 0 , b ≠ 1, and x is any real number

- a is the initial value of f(x) ⇒ (when x = 0)

- b is the growth factor

- The exponent is x

- If the growth factor (b) is in between 1 and 0 then it is exponential

 decay

* Lets solve the problem

∵ f(x)=3(\frac{1}{3})^{x}

- Lets find the initial value

∵ At the initial position x = 0

∴ f(0)=3(\frac{1}{3})^{0}=3(1)=3

* The initial of f(x) is 3

∵ b = 1/3

∵ b is the growth factor of the function

* The growth value of the function is 1/3

∵ b = 1/3

∵ 0 < b < 1

∴ The function is exponential decay

* f(x) shows exponential decay

- A vertical stretching is the stretching of the graph away from the x-axis

- If k > 1, the graph of y = k•f(x) is the graph of f(x) vertically stretched

∵ f(x)=(\frac{1}{3})^{x}

∵ Its parent function is f(x)=3(\frac{1}{3})^{x}

∴ k = 3

∵ k > 1

∴ the function is stretched vertically

* The function is a stretched of the function f(x)=(\frac{1}{3})^{x}

∴ The true statements are:

# The growth value of the function is 1/3

# f(x) shows exponential decay

# The function is a stretched of the function f(x)=(\frac{1}{3})^{x}

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Answer:

6 hrs and 30 minutes

Step-by-step explanation:

Because math:

325/50=6.5

4 0
3 years ago
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Raju borrows rupees 16000 for 2years. the rate of interest for two successive years are 10% and 12%. If he repays rupees 5600 at
Marina86 [1]
Answer is 12,151 rupees.

16000 rupees : 24(bc 2 years)=666 rupees per month.

666 rupees + 10% of the interest rate for the first year= 732 rupees per month for the first year.

For the first year he had to pay 8792 rupees in total.

For the second year he had to pay 8959 bc the interes rate was 12% for the second year.

He only paid 5600 rupees.

8792 rupees + 8959 rupees = 17,751 rupees.

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Thank you
4 0
3 years ago
F(x) = x^2+ 2x-5
Mekhanik [1.2K]

Answe

Step-by-step explanation:

B

4 0
2 years ago
You are a researcher studying the lifespan of a certain species of bacteria. A preliminary sample of 35 bacteria reveals a sampl
arlik [135]

Answer:

The sample size should you gather to achieve a 0.45 hour margin of error

(n) = 411

Step-by-step explanation:

<u>Step(i)</u>

Given data a preliminary sample of 35 bacteria reveals a sample mean of  x = 74  with a standard deviation of s = 5.4

Given the margin of error = 0.45

The degrees of freedom = n-1 = 35-1=34

The 90% of level of significance of t- distribution

t₀.₁₀ = 1.69 ( from table at 34 degrees of freedom at 0.10 level of significance)

<u>Step(ii)</u>

Margin of error = 1.69S / √n

Given data sample standard deviation S =5.4 hours.

margin of error = o.45

Margin of error   = \frac{2S}{\sqrt{n} }

use this formula to determine the sample size

√n = 1.69X5.4/0.45

√n = 20.28

squaring on both sides n= 411.27≅411

<u>Conclusion</u>:-

The sample size should you gather to achieve a 0.45 hour margin of error

(n) = 411

3 0
3 years ago
Find all the zeros of the following function<br> Y=x^4+6x^3+6x^2+6x+5
boyakko [2]

Answer:

Then the four zeros of the given polynomial are {-1, -5, -1, +1}

Step-by-step explanation:

First, make an educated guess regarding the first zero of this polynomial.  Since the constant term is 5, likely zeros are -1, 1, -5 and 5.  Let's check out the possible zero -1, using synthetic div.:

-1   /   1   6   6   6   5

             -1   -5  -1   -5

    --------------------------

        1     5    1    5   0    These are the coefficients of the quotient.

Because the remainder is zero, we know that -1 is a zero of the given polynomial.

Next, let's determine whether -5 is a zereo of the above quotient:

    ------------------------------

-5   /  1    5    1    5

              -5   0  -5

     -------------------------------

        1      0    1    0  Because the remainder is zero, -5 is a zero.


Here the quotient is 1x^2 - 1^2, which factors into (x+1)(x-1)

Setting this result = to 0, we get x = -1 and x = + 1.

Then the four zeros of the given polynomial are {-1, -5, -1, +1}

8 0
3 years ago
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