Answer
(a) About 9.821 meters per second squared.
(b)About 9.821 meters per second squared.
(c) About 9.794 meters per second squared.
(d) The horizontal asymptote will be y = 0.
(e) g(h)=0 isn't theoretically possible. However, as the value of the height gets bigger, it approaches zero acceleration due to gravity, so at very high altitudes the acceleration due to gravity is practically zero. This is the case in real life: when one reaches space, there is very little gravity.
Work Step by Step
(a) Solve g(0):
$g(0)=\dfrac{3.99\times 10^{14}}{(6.374\times10^6+0)^2}$
$g(0)=\dfrac{3.99\times 10^{14}}{(6.374\times10^6)^2}$
$g(0)=\dfrac{3.99\times 10^{14}}{4.063\times10^{13}}\approx9.821$ meters per second squared.
(b) Solve g(443):
$g(443)=\dfrac{3.99\times 10^{14}}{(6.374\times10^6+443)^2}$
$g(443)=\dfrac{3.99\times 10^{14}}{4.063\times10^{13}}\approx9.821$ meters per second squared.
(c) Solve g(8848):
$g(8848)=\dfrac{3.99\times 10^{14}}{(6.374\times10^6+8848)^2}$
$g(8848)=\dfrac{3.99\times 10^{14}}{4.074\times10^{13}}\approx9.794$ meters per second squared.
(d) The degree of the denominator is greater than the degree of the numerator, so the horizontal asymptote will be y = 0.
(e) g(h)=0 isn't theoretically possible. However, as the value of the height gets bigger, it approaches zero acceleration due to gravity, so at very high altitudes the acceleration due to gravity is practically zero. This is the case in real life: when one reaches space, there is very little gravity.
