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!

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