What is f(5) if f(1) = 3.2 and f(x + 1) = 5/2(f(x))? i need one term from this

Question

 PLEASE ANSWER SOON

THANK YOUUUU

Answer 1

f(x+1) = 2.5f(x) is an example of a recursion formula

 

Use what we know about f(1) to find f(2).  Then use f(2) to find f(3), etc.

 

f(1) = 3.2

 

f(2) = f(1+1) = 2.5f(1) = 2.5(3.2) = 8

 

f(3) = f(2+1) = 2.5f(2) = 2.5(8) = 20

 

f(4) = f(3+1) = 2.5f(3) = 2.5(20) = 50

 

f(5) = f(4+1) = 2.5f(4) = 2.5(50) = 125

 

 

Answer 2

f(1)=3.2  is an initial value condition    means that when x=1, f(x)=3.2

 

 

Plugging in,

 

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

 

f(1 + 1) = (5/2)(3.2)

 

f(2) = 8

 

 

Next, we find the slope between (1, 3.2) and (2, 8).

 

m = (8 - 3.2) / (2 - 1)

m = 4.8

 

 

Next, use the point-slope form of the line.  I assume it is a line.  You did not specify in question.

 

f(x) - f₁(x) = m(x - x₁)

 

f(x) - 8 = 4.8(x - 2)

 

f(x) = 4.8(x - 2) + 8

 

f(x) = 4.8x - 1.6

 

 

Evaluate the bolded f(x) when x=5 to get your f(5).