Question

1. the approximate distance above sea level, d, in kilometres, is given by the formula $d = \frac{500\log_{10}(p - 2)}{27}$, where p is the atmospheric pressure in kilopascals. grassi lakes in canmore alberta has a distance above sea level of 1.5 km. determine the atmospheric pressure at grassi lakes. 4 marks

Explanation:

Step1: Substitute d=1.5 into formula

$$1.5 = \frac{500\log_{10}(P-2)}{27}$$

Step2: Isolate the log term

Multiply both sides by 27:
$$1.5 \times 27 = 500\log_{10}(P-2)$$
$$40.5 = 500\log_{10}(P-2)$$
Divide by 500:
$$\log_{10}(P-2) = \frac{40.5}{500} = 0.081$$

Step3: Convert log to exponential form

$$P-2 = 10^{0.081}$$
Calculate $10^{0.081} \approx 1.205$

Step4: Solve for P

$$P = 1.205 + 2$$

Answer:

The atmospheric pressure at Grassi Lakes is approximately 3.21 kiloPascals (rounded to two decimal places, or 3.2 kiloPascals rounded to one decimal place).