Answer:
The population will be 240,116
Step-by-step explanation:
Exponential growth can be represented by the expression:
where:
is the population at time (t)
is the initial value of the population
"r" is the annual rate of growth (written in decimal form)
and "t" is the time in years.
Therefore in this situation, P(16) is what we want to find [the population after 16 years]
the initial population is 110,000
the rate of growth is 0.05 [decimal form of 5%]
and t is 16 years.
Replacing all these in the given functional form gives:
<h3>
Answer: 41</h3>
Work Shown:
f(x) = 6x^2 - 13
f(x) = 6(x)^2 - 13
f(-3) = 6(-3)^2 - 13 ... replace every x with -3; use PEMDAS to simplify
f(-3) = 6(9) - 13
f(-3) = 54 - 13
f(-3) = 41
-16t^2 + 25t + 8 = 10
-16t^2 + 25t - 2 = 0
t = 1.48 seconds
Answer: dr/dt = 9/(24pi) cm per minute
9/(24pi) is approximately equal to 0.119366
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Work Shown:
Given info
dS/dt = 18 cm^2/min is the rate of change of the surface area
r = 6 cm is the radius, from the fact that the diameter is 12 cm
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Use the surface area equation given, apply the derivative, plug in the given values and then isolate dr/dt which represents the rate of change for the radius
S = 4*pi*r^2
dS/dt = 2*4*pi*r*dr/dt
dS/dt = 8*pi*r*dr/dt
18 = 8*pi*6*dr/dt
18 = 48*pi*dr/dt
48pi*dr/dt = 18
dr/dt = 18/(48pi)
dr/dt = (9*2)/(24*2pi)
dr/dt = 9/(24pi)
The units are cm per minute, which can be written as cm/min.
