The population Pa of insect A after t years is given by the equation
Pa = 1.3(1-0.038)^t
while the population Pb of insect B after t years is
Pb = 2.1(1-0.046)^t
We equate the above expressions to find the number of years t it will take the two populations to be equal:
Pa = Pb
1.3(1-0.038)^t = 2.1(1-0.046)^t
1.3(0.962)^t = 2.1(0.954)^t
These are the equations that can be used to determine how long it will be before the populations of the two species are equal.
We can now solve for t:
(0.962)^t / (0.954)^t = 2.1/1.3
(0.962/0.954)^t = 2.1/1.3
After taking the log of both sides of our equation, number of years t is
t = log (2.1/1.3) / log (0.962/0.954)
t = 57 years
Therefore, it will take 57 years for the population of insect A to equal the population of insect B.
Answer:
71°
Step-by-step explanation:
12/36 = 1/3
inverse cos(1/3) = 70.53 = 71
Answer:
- 5
Step-by-step explanation:
Note that - (- 12) = + 12
Thus
- 17 - (- 12) = - 17 + 12 = - 5
It looks like Tom subtracted 12 from - 17, that is - 17 - 12 = - 29
Answer:
(1, -3/2)
Step-by-step explanation:
The x coordinate is the same for both endpoints so the x coordinate for the midpoint is 1
The y coordinate for the midpoint is found by adding the two y coordinates and dividing by 2
(2+-5)/2 = -3/2
The midpoint is
(1, -3/2)
