What is f(5) if f(1)=3.2 and f(x+1)=5/2(f(

Work Shown:

f(1) = 3.2 is the first term

Use this to find f(2). Plug in x = 1

f(x+1) = (5/2)*f(x)

f(1+1) = (5/2)*f(1)

f(2) = (5/2)*3.2

f(2) = 2.5*3.2

f(2) = 8

Then use this to find f(3). Plug in x = 2

f(x+1) = (5/2)*f(x)

f(2+1) = (5/2)*f(2)

f(3) = (5/2)*f(2)

f(3) = (5/2)*8

f(3) = 2.5*8

f(3) = 20

Use this to find f(4). Plug in x = 3

f(x+1) = (5/2)*f(x)

f(3+1) = (5/2)*f(3)

f(4) = (5/2)*f(3)

f(4) = (5/2)*20

f(4) = 2.5*20

f(4) = 50

Use this to find f(5). Plug in x = 4

f(x+1) = (5/2)*f(x)

f(4+1) = (5/2)*f(4)

f(5) = (5/2)*f(4)

f(5) = (5/2)*50

f(5) = 2.5*50

f(5) = 125

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

b

step-by-step explanation: