Can the tables of data be modeled by a linear function an ex

Can the tables of data be modeled by a linear function, an exponential function, or neither? Justify your reason. IF the data can be modeled by a linear function or exponential function, give an equation for the function. for each exponential function, state the domain and range, whether the function is growth or decay, and the y-intercept. y = -1/4(10)^x y = 0.25(50)^x y = -4(2/5)^x y = 6(.25)^x Given g(x) = - 1/2 (5)^x + 3 + 4 The parent function is f(x) = Describe the transformations made on the graph of f(x) to get to the graph of g(x). (Use terms such as horizontal translation, vertical translation, reflection, vertical stretch, vertical shrink.) The domain of g(x):. The range of g(x): Equation for the horizontal asymptote:

Solution

If the ratio of dependent values is the same, then the data is modeled by an exponential equation.

If the difference of the yvalues, we must make sure that we examine entries for which the xvalues increase by the same amount.Its a linear function.

1 a) x 0 1 2 3 4   

y 50 45 40.5 36.45 32.805

45/50 = 40.5/45 = 36.45/40.5 = 32.805/36.45 = 0.9

Its an exponential function

y = ab^x

x =0 ; y=50 : a =50

x =1 ; y=45

45 = 50(b)^1 ----> b =0.9

y = 50(0.9)^x

b)   

x 0 1 2 3 4   

y 50 45 40 35 30

45-50 = 40-45 = 35-40 = 30 -35 = -5

Its a linear function

slope = -5 ; y = -5x +c; c =50

y = -5x +50

c)

x 0 1 2 3 4   

y 50 60 72 86.4 103.68

60/50 = 72/60 = 86.4/72 = 103.68/86.4 =1.2

Its an exponential function.

y = ab^x

x =0 ; y=50 : a =50

x =1 ; y=45

60 = 50(b)^1 ----> b =1.2

y = 50(1.2)^x

d)

x 0 1 2 3 4   

y 50 65 84.5 109.85 142.805

65/50 = 84.5/65 = 109.85/84.5 = 142.805/109.85 = 1.3

Its an exponential function

y = ab^x

x =0 ; y=50 : a =50

x =1 ; y=45

65 = 50(b)^1 ----> b =0.9

y = 50(1.3)^x