finding linear/exponential formulas

[santaclaus]

suppose f(-3)=5/8 and f(2)=20. Find a formula for f assuming it is

a. linear y=mx +b so slope was 155/8. If I put it into the formula y=19 3/8x -18 3/4


b. exponential
f(20) =20. P=f(t)=ab^t
f(2)=ab₂=20

f(-3)=ab^-3=5/8
then put one equation over th eother to get b⁵=32, so b=2

is this correct?

[stapel_eliz]

suppose f(-3)=5/8 and f(2)=20. Find a formula for f assuming it is

a. linear y=mx +b so slope was 155/8. If I put it into the formula y=19 3/8x -18 3/4

To find the slope, you need to divide the difference of the y-values by the difference of the x-values.

b. exponential
f(20) =20. P=f(t)=ab^t
f(2)=ab₂=20
f(-3)=ab^-3=5/8
then put one equation over th eother to get b⁵=32, so b=2

Once you've determined that b = 2 (I get the same value, by the way), then back-solve to find the value of "a". Then write the function f(t) = a*b^t, plugging in your values for "a" and "b".