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:
Step-by-step explanation:
2)Cos²x - Sin² x = √2/2
Cos²x - Sin² x = Cos 2x
⇒ Cos 2x = √2/2
General solution for Cos 2x = √2/2 is
Option A
<span>What is the geometric mean for the numbers 175 and 7?
175/x = x/7
x^2 = 7*175
x = 35</span>
Simple interest formula:
Total = start value x (1 + rate x time)
Total = 600 x (1 + 0.12 x 6)
Total = $643.20
answer: B. $643.20