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:
move each point of the triangle 5 units to the right and one unit up.
G is at -3,-1
-3+5 = 2
-1+1 = 0
2,0 is the coordinates of G' or the new G
T is at -1,-1
-1+5 = 4
-1+1 = 0
4,0 is the coordinates of T' or the new T
Last of all, B is at -3,-5
-3+5 = 2
-5+1 = -4
2,-4 is the coordinates of the B' or the new B.
Step-by-step explanation:
This means that point P lies on GK where the ratio between the length of GP to the length of PK is:
GP/PK = 2/3
To better understand this, assume that the length of GK is 5 cm. Applying the given ratio, we will find that:
GP = 2 cm and PK = 3cm
Answer:
If a<b, x<2
If a>b, x>2
Step-by-step explanation:
ax-bx>2a-2b, (a-b)x>2(a-b)
If a>b, x>2(a-b)/(a-b)=2
If a<b, x<2(a-b)/(a-b)=2
Sometimes should be the answer
