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soldier1979 [14.2K]
2 years ago
6

Several ordered pairs from a continuous exponential function are shown in the table.

Mathematics
2 answers:
Klio2033 [76]2 years ago
6 0

Answer:

The Answer is C!

The domain is the set of real numbers, and the range is y > 0.

Step-by-step explanation:

Sunny_sXe [5.5K]2 years ago
4 0

Answer:

The domain is {x : x ∈ R} , the range is {y : y > 0}

Step-by-step explanation:

* Lets explain how to solve the problem

- The general form of the continuous exponential function is

  y=a(e)^{kx} where a is the initial value and k is the growth factor

- We have some ordered pairs from the continuous exponential

  function

- The ordered pairs are:

  (0 , 4) , (1 , 5) , (2 , 6.25) , (3 , 7.8125)

- Lets substitute the values of x and y in the equation to find a , e^{k}

∵ y=a(e)^{kx}

∵ x = 0 and y = 4 ⇒ 1st ordered pair

- Substitute x and y in the equation

∴ 4=a(e)^{k(0)}

∴ 4=a(e)^{0}

- The value of e^{0} = 1

∴ a = 4

- Substitute the value of a in the equation

∴ y=4(e)^{kx}

∵ x = 1 and y = 5 ⇒ 1st ordered pair

- Substitute x and y in the equation

∴ 5=4(e)^{k(1)}

∴ 5=4(e)^{k}

- Divide both sides by 4

∴ e^{k} = 1.25

- Substitute the value of e^{k} in the equation

∴ y=4(1.25)^{x}

- The domain of the function is all the values of x which make the

  function defines

- The range is the values of y corresponding to x

∵ There is no value of x makes the function undefined

∴ <u><em>The domain is all real numbers</em></u>

∵ y never takes a negative value

∴ <u><em>The range is all the real positive numbers</em></u>

* <em>The domain is {x : x ∈ R} , the range is {y : y > 0}</em>

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