How to complete a table of values of an exponential function?

Question

I got this question from my teacher and I tried to solve but no luck! the question given is:

Toss 100 pennies and remove all of the ‘heads’. Toss the remaining pennies, and again, remove all heads. Repeat this process until all coins have been removed.

A. Record the number of pennies tossed for each trial in a table.

\begin{array}{|l|l|} \hline \text{Number of trial} & \text{Number of pennies tossed} \\ \hline 1 & 100 \\ 2 & \\ 3 & \\ 4 & \\ 5 & \\ 6 & \\ 7 & \\ 8 & \\ 9 & \\ 10 & \\ \hline \end{array}

B. Graph the data and draw a smooth curve through the points.

C. Explain why this data can be modeled by an exponential function.

Based on what I know, we should use the general form of an exponential function which is $y=a\cdot b^x + c$

I think C, in this case, is 100

and from the pattern, we can divide the second value of Y by the first value of Y then we get the common ratio that can help to complete the table of value.

In this question, I have only one Y-value!

Answer 1

The word "record" means that you should observe what happens and write it down, not try to predict it. Indeed, notice that there isn't any way to predict the first new value - you can't predict how many pennies will come down heads unless you try it and see!

The problem seems to be literally asking you to flip 100 pennies, remove the ones that come up heads, and repeat, writing down the results as you go.

Answer 2

Why not follow the instructions?

This is a physical experiment, which includes documenting and analyzing your observations, fitting them to a mathematical model.

Your general function seems to be $$ y(x) = a \cdot b^x $$

Think about using a half logarithmic plot ($x$ vs $\log y$) so you can interpolate with a simple straight line.