To convert the exponential function $y = 33 \times 10^{-0.9x}$ into a linear function in a logarithmic scale, we'll follow these steps:

1. Take the logarithm (base 10) of both sides: $\log_{10}(y) = \log_{10}\left(33 \times 10^{-0.9x}\right)$

2. Use logarithm properties: $\log_{10}(y) = \log_{10}(33) + \log_{10}\left(10^{-0.9x}\right)$

   $\log_{10}(y) = \log_{10}(33) - 0.9x$

3. Calculate $\log_{10}(33)$: $\log_{10}(33) \approx 1.5$

4. Substitute back into the equation: $\log_{10}(y) \approx 1.5 - 0.9x$

So, the linear form of the given exponential function on a logarithmic scale is:

$\log_{10}(y) = 1.5 - 0.9x$

This represents a straight line in a logarithmic plot, where the slope is $-0.9$ and the intercept is $1.5$.

Would you like further details or have any questions?

Here are 5 related questions:

1. How does changing the base of the logarithm affect the linear representation?
2. What is the significance of the slope $-0.9$ in the logarithmic scale?
3. How can you determine the original function from the linear logarithmic form?
4. What would the graph of $\log_{10}(y) = 1.5 - 0.9x$ look like?
5. How would you approach this problem using natural logarithms instead of common logarithms?

Tip: Remember, taking the logarithm of an exponential function linearizes the expression, making it easier to analyze relationships like growth and decay.