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
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 ,
∵
∵ x = 0 and y = 4 ⇒ 1st ordered pair
- Substitute x and y in the equation
∴
∴
- The value of = 1
∴ a = 4
- Substitute the value of a in the equation
∴
∵ x = 1 and y = 5 ⇒ 1st ordered pair
- Substitute x and y in the equation
∴
∴
- Divide both sides by 4
∴ = 1.25
- Substitute the value of in the equation
∴
- 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>