Answer:
The population will become 840 million in 2019.
Step-by-step explanation:
Given:
The exponential model of population is given as:
Here, 't' is in years measured since 2003.
This means for the year 2003, t = 0 and so on.
Now, in order to get the year when the population is 840 million, we need to plug in 840 for 'A' and solve for 't'. Therefore,
Taking natural log on both sides, we get:
Therefore, 16 years after 2003, the population will be 840 million.
So, the year is equal to 2003 + 16 = 2019.
Hence, in the year 2019, the population will become 840 million.
Since the point is equidistant from (3,8) and (-2,5) on the y-axis, we are talking about the middle point, so:
Therefore the coordinates are:
(0.5,6.5)
Answer:
Step-by-step explanation:
Here's the formula for the volume of a right circular cylinder:
Here's what we are given and what we need to find:
Given that d = 10 cm, h = 20 cm, dd/dt = 1 cm/sec
Need to find dh/dt when V is constant
Since our formula has a radius in it and not a diameter but the info given is a diameter, we can use the substitution that
so
Now we can rewrite the formula in terms of diameter:
which simplifies down to
Now we will take the derivative of this equation with respect to time using the product rule. That derivative is
Now we can fill in our values. Keep in mind that if the volume is constant, there is no change in the volume, so dV/dt = 0.
and
Multiply both sides by pi/4 to get
and solve for dh/dt:
Interpreted within the context of our problem, this means that the volume will be constant at those given values of diameter and height when the liquid in the cylinder is dropping at a rate of 4 cm/sec.