The weather satellite NOAA-15 orbits the Earth every 101 min at an altitude of 807 km as shown in the figure. The cameras on the satellite have a maximum range defined by the set of lines tangent to the Earth from the satellite. Using the radius of the Earth as 6357 km , approximate the length of the arc from A to B to the nearest kilometer. This is the maximum distance along the surface of the Earth' seen" by the satellite's cameras.
The weather satellite NOAA-15 orbits the Earth every 101 min at an altitude of 807 km as shown in the figure. The cameras on the satellite have a maximum range defined by the set of lines tangent to the Earth from the satellite. Using the radius of the Earth as 6357 km , approximate the length of the arc from A to B to the nearest kilometer. This is the maximum distance along the surface of the Earth' seen" by the satellite's cameras.
The weather satellite NOAA-15 orbits the Earth every
101
min
at an altitude of
807
km
as shown in the figure. The cameras on the satellite have a maximum range defined by the set of lines tangent to the Earth from the satellite. Using the radius of the Earth as
6357
km
, approximate the length of the arc from
A
to
B
to the nearest kilometer. This is the maximum distance along the surface of the Earth' seen" by the satellite's cameras.
3. We'd like to know the first time when the population reaches 7000 people. First, graph the
function from part (a) on your calculator or Desmos. In the same window, graph the line y =
7000. Notice that you will need to adjust your window so that you can see values as big as
7000! Investigate the intersection of the two graphs. (This video shows you how to find the
intersection on your calculator, or in Desmos just hover the cursor over the point.) At what
value t> 0 does the line intersect with your exponential function? Round your answer to two
decimal places. (You don't need to show work for this part.) (2 points)
Suppose the planet of Tattooine currently has a population of 6500 people and an annual growth rate of
0.35%. Use this information for all the problems below.
1. Find an exponential function f(t) that gives the population of Tattooine t years from now. (3
points)
A house was valued at $95,000 in the year 1988. The value appreciated to $170,000 by the year 2007.
A) If the value is growing exponentially, what was the annual growth rate between 1988 and 2007?
Round the growth rate to 4 decimal places.
r =
B) What is the correct answer to part A written in percentage form?
r = 3
%.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Fundamental Theorem of Calculus 1 | Geometric Idea + Chain Rule Example; Author: Dr. Trefor Bazett;https://www.youtube.com/watch?v=hAfpl8jLFOs;License: Standard YouTube License, CC-BY