Answer:
P(t) = 2093e^(42t).
Step-by-step explanation:
The population of this town can be modeled by the following differential equation
dP/dt = Pr
where r is the growth rate in people a year.
We can solve this differential equation by the separation of variables method.
dP/P = rdt
Integrating both sides, we have:
ln P = rt + P0
where P0 is the initial population
To isolate P, we do this:
e^(ln P) = e^(rt + P0)
P(t) = P0e^(rt).
We have that the population increases by 42 people a year, so r = 42. We also have that the population at time t = 0 is 2093 people, so P0 = 2093.
So the formula for the population, P, of the town as a function of year t is P(t) = 2093e^(42t).
Answer:
x=35°
Step-by-step explanation:
145°+110°+70°=325°
360°-325°=35°
Answer:
The population changed by 20% in 3 years
Step-by-step explanation:
The percentage change, is given by the following equation;
The given parameters are;
The initial population of the town = 35,000
The final population of the town = 42,000
The percentage change in the population is therefore;
The population changed (increase) by 20% in 3 years.
Answer:
Add 6,then add 7 , add 6,then add 20 and add 6 and add 46 and so on
Answer:
(3x-4)(x-5)
Step-by-step explanation:
This is in the form
ax²+bx+c.
To factor this, we find factors of a·c that sum to b; this means factors of 3(20) = 60 that sum to -19:
60 = 1(60) or -1(-60); 2(30) or -2(-30); 3(20) or -3(-20); 4(15) or -4(-15); 5(12) or -5(-12); 6(10) or -6(-10). The only of these that sum to -19 are -4 and -15. This means we will split up -19x into -4x and -15x:
3x²-4x-15x+20
Next we group the first two terms and the last two terms:
(3x²-4x)+(-15x+20)
Factor out the GCF of each group. For the first group, this is x:
x(3x-4)
For the second group, this is -5:
-5(3x-4)
The common factor for these two groups is (3x-4):
(3x-4)(x-5)