Questions: Convert the equation (f(t)=253 e^-0.27 t) to the form (f(t)=a b^t) a= b=

Transcript text: Convert the equation $f(t)=253 e^{-0.27 t}$ to the form $f(t)=a b^{t}$ \[ \begin{array}{l} a= \\ b= \end{array} \]

Solution

Solution Steps

Step 1: Identify the initial value $a$

The initial value $a$ is the coefficient in front of the exponential term in the given function $f(t) = 253 e^{-0.27 t}$. Therefore, we have: \[ a = 253 \]

Step 2: Determine the new base $b$

To find the new base $b$, we need to rewrite the exponent's base $e$ to the power of the decay rate as a single number. This can be done by evaluating $e^{-0.27}$: \[ b = e^{-0.27} \approx 0.7634 \]

Final Answer

The equation $f(t) = 253 e^{-0.27 t}$ can be converted to the form $f(t) = a b^t$ with: \[ \begin{array}{l} a = 253 \\ b \approx 0.7634 \end{array} \] \[ \boxed{a = 253, \, b \approx 0.7634} \]

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