Question

If f(3)=5 and f(4)=8 find f(7) and f(8)

Answer 1

F(3) = 5 [5-3=2 diff]
f(4) = 8 [8-4=4 diff] (or 2 times larger than f(3)’s diff)

If that holds true, then continue the pattern:

f(5) = 13 [2 times f(4) diff = 8 so 5 + 8 = 13]
f(6) = 22
f(7) = 39
f(8) = 72

The only problem with my answer is that it could be times 2 or ^2. My answer above assumes times 2.

Answer 2

Answer:  f(7) = 17   &   f(8) = 20

Step-by-step explanation:

We can use f(3) = 5 and f(4) = 8 to write points that we can turn into an equation, and then solve for f(7) and f(8).

f(3) = 5 can be written as (3 , 5)

f(4) = 8 can be written as (4 , 8)

The slope of this line using the slope (y₂ - y₁) ÷ (x₂ - x₁)  = (8 - 5) ÷ (4 - 3)

                                                                                          =  3

The equation of the line can be written in the point-slope form (y - y₁) = m(x - x₁)); where (x₁ , y₁) = (3 , 5):

             y - 5 = 3 (x - 3)

Now, f(7) occurs when x = 7

             y - 5 = 3 (7 - 3)

             y - 5 = 12

                  y  = 17

                       ∴  f(7) = 17

Now, f(8) occurs when x = 8

            y - 5 = 3 (8 -3)

            y - 5 = 15

                 y = 20

                     ∴ f(8) = 20