Question

please help with number 9 and 10?

Answer 1

I think number 9 is 11,200
and I think 10 is in 2 days from day 3 but i'm not sure

Answer 2

That is correct for #9 although it would be nice if the work is shown.

Answer 3

For 12, it might be easier to simply extend the table. You already did altitude at end of day #4 to be 11,200 ft. What is the altitude at the end of day #5? Will the peak have been reached by then? Can the peak be reached on day #6? Can the peak ever be reached?

A slightly longer method might be as follows:
The distance climbed each day is an arithmetic sequence with first term \(a_1=4,000\) and common difference \(d=−800\). Use the formula for the sum of the first n terms of an arithmetic sequence to find n.
\[
S_n = \frac n 2 \{2a_1 + (n-1)d\} \ge 12,388 \\
\frac n2\{ 2*4000 + (n-1)(-800)\} \ge 12,388
\]Solve for n. Does a solution exist?