Answer:
Point (1 , 0.75) lies on the graph of the function ⇒ last answer
Step-by-step explanation:
* Lets revise the exponential function
- An exponential function with base b is defined by f (x) = ab^x
where a ≠0, b > 0 , b ≠1, and x is any real number.
- The base, b, is constant and the exponent, x, is a variable.
- The graph of it in the attached figure
- Features (for this graph):
• The domain is all Real numbers.
• The range is all positive real numbers (not zero).
• The y-intercept at (0 , 1.5). Remember any number to
the power of zero is 1.
• Because 0 < b < 1, the graph decreases (b = 1/2)
* Now lets check which point lies on the graph
- Substitute the value of x of the point, in the function
- If the answer is the same as y, then the point lies on the graph of
the function
∵ y = 1.5(1/2)^x
∵ x = -3
∴ y = 1.5(1/2)^(-3) = 187.5 ≠ 1
∴ Point (-3 , 1) does not lie on the graph of the function
∵ x = 2
∴ y = 1.5(1/2)² = 3/8 ≠ 5
∴ Point (2 , 5) does not lie on the graph of the function
∵ x = -2
∴ y = 1.5(1/2)^-2 = 6 ≠ 3
∴ Point (-2 , 3) does not lie on the graph of the function
∵ x = 1
∴ y = 1.5(1/2)^1 = 0.75
∴ Point (1 , 0.75) lies on the graph of the function
The line equation in slope-intercept form is given by
where b is the y-intercept and m is the slope.
Then, we need to convert the given equation into the slope-intercept form. Then, by subtracting 10x to both sides, we have
and by dividing both sides by 2, we get
By comparing this result with the first equation, we can see that the slope is m= -5. So, the answer is: -5