Soles analysis. Monthly sales of an SUV model are expected to increase at the rate of S ′ ( t ) = − 24 t 1 / 3 SUVs per month, where t is time in months and S ( t ) is the number of SUVs sold each month. The company plans to stop manufacturing this model when monthly sales reach 300 SUVs. If monthly sales now ( t = 0) are 1,200 SUVs, find S ( t ). How long will the company continue to manufacture this model?
Soles analysis. Monthly sales of an SUV model are expected to increase at the rate of S ′ ( t ) = − 24 t 1 / 3 SUVs per month, where t is time in months and S ( t ) is the number of SUVs sold each month. The company plans to stop manufacturing this model when monthly sales reach 300 SUVs. If monthly sales now ( t = 0) are 1,200 SUVs, find S ( t ). How long will the company continue to manufacture this model?
Solution Summary: The author explains how the function S(t) can be used to find the time taken by the company to manufacture the model.
Soles analysis. Monthly sales of an SUV model are expected to increase at the rate of
S
′
(
t
)
=
−
24
t
1
/
3
SUVs per month, where t is time in months and S(t) is the number of SUVs sold each month. The company plans to stop manufacturing this model when monthly sales reach 300 SUVs. If monthly sales now (t = 0) are 1,200 SUVs, find S(t). How long will the company continue to manufacture this model?
According to Newton's law of universal gravitation, the force F between two bodies of constant mass
GmM
m and M is given by the formula F =
, where G is the gravitational constant and d is the
d²
distance between the bodies.
a. Suppose that G, m, and M are constants. Find the rate of change of force F with respect to
distance d.
F' (d)
2GmM
b. Find the rate of change of force F with gravitational constant G = 6.67 × 10-¹¹ Nm²/kg², on
two bodies 5 meters apart, each with a mass of 250 kilograms. Answer in scientific notation,
rounding to 2 decimal places.
-6.67x10
N/m syntax incomplete.
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