## finding linear/exponential formulas

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
santaclaus
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Joined: Tue Mar 03, 2009 12:17 am
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### finding linear/exponential formulas

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)=abt
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
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
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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)=abt
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*bt, plugging in your values for "a" and "b".