The compound inequality can be rewritten as two separate inequalities. Make a table and use it to solve for these inequalities separately.
14.39≤ P≤ 26.65
Practice makes perfect
We have been given a function A(P) which models the altitude as a function of barometric pressure P.
A(P)= 90 000 - 26 500 ln(P)
We need to find the corresponding barometric pressure for the base and peak of Kilimanjaro represented by a compound inequality.
3000≤ A(P)≤ 19 340
⇓
3000≤ 90 000 - 26 500 ln(P)≤ 19 340
We will split this compound inequality into two inequalities, and solve them one at the time.
Lower Altitude
Let's begin by solving the inequality representing the barometric pressure for the base of Kilimanjaro.
3000 ≤ 90 000-26 500ln(P)
First we need to create a table of values for the function A(P). We then first press Y= on the calculator and write the equation on the first row. Then we press 2nd and then GRAPH to get a table of values.
To change the table settings, press 2nd and WINDOW. Then change TblStart to 30 and â–³ Tbl to - 1. To get the table of values we once more press 2nd and then GRAPH.
We will start by finding the corresponding pressure to A(P)=3000. To find it we need to find values for the function in the interval 26 < P < 27. Let's push 2nd and WINDOW. The values in the table indicates that a suitable value for â–³ Tbl is - 0.01 and for TblStart is 26.5.
The function's value is about 3000 at P≈ 26.65.
Higher Altitude
We now want to know the barometric pressure at the top of Kilimanjaro. To find that we need to solve the corresponding inequality.
90 000-26 500ln(P)≤ 19 340
We change the table setup once more so that â–³ Tbl=- 1. This will make it easier to find where we should be looking. Having determined where we should look, choose increasingly smaller increments of x.
The function's value is about 19 340 at P≈ 14.39.
Combining the Inequalities
We have found the barometric pressure at the base and at the peak of Kilimanjaro.
Base:& P≈ 26.65
Peak:& P≈ 14.39
Using these values, we can write the values of normal barometric pressure on Kilimanjaro as a compound inequality.
14.39≤ P≤ 26.65
