SOLUTION: 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.

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.

RELATED QUESTIONS
Convert the equation f(t) = 116(0.69)^t to the form f(t) = ae^kt Find a = ? and k = ? (answered by MathLover1,math_tutor2020)

Evaluate f(0), f(1),and f(2). Round your answer to three decimal places. A) Express... (answered by Shin123)

Convert the equation f(t)=242(1.16)^t to the form f(t)=ae^(kt) (answered by josgarithmetic)

Find the value of the growth factor b, in the exponential function, f(t)=ab^t , that... (answered by josgarithmetic)

convert the given exponential function to the form indicated. Round all coefficients to... (answered by math_tutor2020)

Convert the given exponential function to the form indicated. Round all coefficients to... (answered by solver91311)