Answer:
Step-by-step explanation:
The growth of the population can be modeled by the following differential equation:
Where r is the growth rate, P is the population, and t is the time measures in months.
I am going to solve the above differential equation with the separation of variables method.
Integrating both sides:
Where P(0) is the initial condition
We need to isolate P in this equation, so we do this
So
The problem states that P(0)=3000, so:
The problem wants us to find the value of r:
It states that the population doubles in size from 3000 to 6000 in a 6- month period, meaning that P(6) = 6000. So
To isolate 6r, we apply ln to both sides.
r = 0.1155
The particular solution to the differential equation with the initial condition P(0)=3000 is:
Canceled cheques are negotiable at the bank for the face value is False
Answer:
Step-by-step explanation:
20,24,25,27,31,35,38
minimum;20
medium: 27
maximum: 38
lower quartile: 24
upper quartile:35
put numbers in number order
the first number is the minimum, the last number is the maximum. the middle number "split" is the median.
quartiles are the numbers in the middle of the data you just "split"
(so like a quarter)
i may be wrong i haven't done this in years
Answer:
Step-by-step explanation:
Surface area is the area times all the faces
A.) To find the maximum height, we can take the derivative of h(t). This will give us the rate at which the horse jumps (velocity) at time t.
h'(t) = -32t + 16
When the horse reaches its maximum height, its position on h(t) will be at the top of the parabola. The slope at this point will be zero because the line tangent to the peak of a parabola is a horizontal line. By setting h'(t) equal to 0, we can find the critical numbers which will be the maximum and minimum t values.
-32t + 16 = 0
-32t = -16
t = 0.5 seconds
b.) To find out if the horse can clear a fence that is 3.5 feet tall, we can plug 0.5 in for t in h(t) and solve for the maximum height.
h(0.5) = -16(0.5)^2 + 16(-0.5) = 4 feet
If 4 is the maximum height the horse can jump, then yes, it can clear a 3.5 foot tall fence.
c.) We know that the horse is in the air whenever h(t) is greater than 0.
-16t^2 + 16t = 0
-16t(t-1)=0
t = 0 and 1
So if the horse is on the ground at t = 0 and t = 1, then we know it was in the air for 1 second.
