https://file.aiquickdraw.com/mathbot/file/1729571725852iy1ycxog.jpg

The problem in the image asks to convert the given exponential function into a different form and to round coefficients to four significant digits.

The given function is:

\[
f(t) = 5(0.973)^t
\]

It needs to be converted to the form:

\[
f(t) = Q_0 e^{-kt}
\]

### Steps to solve:

1. The general form \( f(t) = Q_0 e^{-kt} \) is an exponential decay model. Here, \( Q_0 \) is the initial quantity and \( k \) is the decay rate.
   
2. Start by rewriting \( 5(0.973)^t \) in terms of \( e^{-kt} \):
   
   \[
   0.973^t = e^{t \ln(0.973)}
   \]

3. Now substitute this into the given equation:

   \[
   f(t) = 5 \cdot e^{t \ln(0.973)}
   \]

4. From this, we can see that:

   \[
   Q_0 = 5 \quad \text{and} \quad k = -\ln(0.973)
   \]

5. Compute \( k \):

   \[
   k = -\ln(0.973) \approx -(-0.02734) = 0.02734
   \]

6. Therefore, the final form of the equation is:

   \[
   f(t) = 5 e^{-0.02734 t}
   \]

Rounded to four significant digits, the solution is:

\[
f(t) = 5 e^{-0.02734 t}
\]

Let me know if you'd like further details or have any questions!

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### Related Questions:

1. How does the base of a natural logarithm help in converting exponential functions?
2. Why is \( k \) considered a decay constant in the equation \( f(t) = Q_0 e^{-kt} \)?
3. What happens when the base of the exponent is larger than 1 instead of less than 

Convert the given exponential function to the form indicated. Round all coefficients to four significant digits. f(t) = 5(0.973)^t ; f(t) = Q_0 e^{-kt}

Learn how to convert the exponential function f(t) = 5(0.973)^t into the form f(t) = Q_0 e^{-kt}, rounding all coefficients to four significant digits. This problem involves exponential decay and logarithmic properties, suitable for high school and early college-level students.

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