Answer:
= 173.903t
Explanation:
The given equation is: f(t) = 227e^(b*t)
To convert it to the form f(t) = ab, we need to write it in the form of f(t) = a * e^(k*t), where a and k are constants.
Let's start by taking the natural logarithm (ln) of both sides:
ln(f(t)) = ln(227e^(b*t))
Using the properties of logarithms, we can simplify this to:
ln(f(t)) = ln(227) + ln(e^(b*t))
ln(f(t)) = ln(227) + b*t
Now, let's define a new constant, k = b, and rewrite the equation in terms of a and k:
ln(f(t)) = ln(a) + k*t
where a = 227 and k = -0.09
Taking the exponential of both sides, we get:
f(t) = e^(ln(a) + k*t)
f(t) = e^(ln(a)) * e^(k*t)
f(t) = a * e^(k*t)
Substituting the values of a and k, we get:
f(t) = 227 * e^(-0.09*t)
Therefore, the equation f(t) = ab is:
f(t) = 227e^(-0.09t) ≈ 173.903t (rounded to three decimal places)