Graph the exponential model ! needed !

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

(d)

step-by-step explanation:

given: the line in the graph passes through points (5,30) and (6,26).

then, the equation of line is:

now, put y=a(n) and x=n,

hence, option d is correct.