Question 1204987: Convert the equation f(t) = 166e^-0.23t to the form f(t) = abt^t
Find the value of b and round off to three decimal places.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! to convert from a*e^(bt) to a*c^t, you would do the following.
start with y = a * e^(bt), as in y = 166 * e^(-.23t)
set t = 1 to get y = 166 * e^(-.23).
solve for y to get y = 131.892578.
now start with y = a * b ^ t
when a = 166 and y = 131.892578 and t = 1, you get:
131.892578 = 266 * b ^ 1 which becomes:
131.892578 = 266 * b
solve for b to get:
b = 131.892578 / 266 = .7945336025.
your exponential equation becomes y = 166 * .7945336025 ^ t
when t = 1, you get y = 166 * .7945336025 ^ 1 = 131.892578.
this works for any value of t.
for example, if t = 15, you get:
y = 166 * e ^(-.23 * 15) = 5.269775639.
and you get:
y = 166 * .7945336025 ^ 15 = 5.269775639.
the two forms of the equation are equivalent and give the same answer.
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