Final answer:
To approximate the change in atmospheric pressure, we can use a linear approximation and calculate the difference between the pressures at the given altitudes using the formula p(z)=1000e^(-z/10).
Step-by-step explanation:
To approximate the change in atmospheric pressure when the altitude increases from z=7 km to z=7.02 km using the formula p(z)=1000e^(-z/10), we can use a linear approximation. First, we need to find the pressure at z=7 km and z=7.02 km. Plugging in z=7 into the formula gives us p(7) = 1000e^(-7/10). Plugging in z=7.02, we get p(7.02) = 1000e^(-7.02/10). By calculating the difference between these two pressures, we can approximate the change in atmospheric pressure.