Answer:
105 years
Step-by-step explanation:
Given the function :
Q(t) = 4e^(-0.00938t)
Q = Quantity in kilogram of an element in a storage unit after t years
how long will it be before the quantity is less than 1.5kg
Inputting Q = 1.5kg into the equation:
1.5 = 4e^(-0.00938t)
Divide both sides by 4
(1.5 / 4) = (4e^(-0.00938t) / 4)
0.375 = e^(-0.00938t)
Take the ln of both sides
In(0.375) = In(e^(-0.00938t))
−0.980829 = -0.00938t
Divide both sides by 0.00938
0.00938t / 0.00938 = 0.980829 /0.00938
t = 104.56599
When t = 104.56599 years , the quantity in kilogram of the element in storage will be exactly 1.5kg
Therefore, when t = 105 years, the quantity of element in storage will be less than 1.5kg
Remark
The easiest way to do this is to find the radius of both spheres . That gives you the scale factor. The answer to the next two parts might surprise you.
Step one
Find the volume of the small sphere.
V = 4/3 pi r^3
V = 250 yards^3
pi = 3.14
r = ???
Sub and solve
250 = 4/3 pi * r^3 Multiply both sides by 3/4 to get rid of the fraction on the right.
250 * 3/4 = pi * r^3
187.5 = pi r^3 Divide by pi
187.5 / pi = r^3
59.71 = r^3 Take the cube root of both sides.
cube root (59.71) = cube root(r^3)
r = 3.91
Step 2
find the radius of the large sphere.
I'm just going to give you the answer. Follow the above steps to confirm it.
V = 686 cubic yards
pi = 3.14
r = ??
r = cube root (514.5/3.14)
r = 5.472
Step 3
Find the ratio
r_large/r_small = 5.472/3.91 = 1.3995
I'm going to leave the Area calculations to you
The area ratios should come to 1.96 (about)
The volume ratios should come to 1:2.74
The second graph represents a constant speed of M miles per hour