relative growth rate?

Question

The relative growth rate of the population of Lynton is 0.047 and its current population is P(0) = 83,400

a. Write a differential equation for the population.
b. Find a formula for the population P in terms of t.

Answer 1

Let P stand for P(t).

a.) If the "relative growth rate ... is 0.047," that means that:

(1/P)dP/dt = 0.047, or dP/dt - 0.047 P = 0.

[Either of these would qualify as the differential equation for the population.]

b.) The solution to this differential equation is:

P(t) = P(0) e^(0.047t) = 83,400 e^(0.047t).

Live long and prosper.

P.S. I'm afraid that the second line in the first responder's answer,
"P = P(0)[1.047]^t," is incorrect, even though the first line (stated without giving the differential equation) is O.K.

Answer 2

ok is the decay fee consistent. ok is got here across utilising a logarithmic function... -ok=(organic logarithm of two) / time of the 0.5 existence or by using and tremendous written as -ok=(ln2)/t1/2 be conscious ok is unfavourable by means of fact the manufactured from (ln2)/t1/2 ought to be elevated by using -one million to supply the linked fee consistent in case you have been fixing a nil.5-existence difficulty as you in many circumstances could use this in chemistry or physics you're able to then keep on with this consistent to the formulation: (time)= (extensive kind modern now/extensive kind modern initially) ____________________________________ -ok extensive kind modern many times is composed of the quantity of the substance in contact contained in the difficulty like milligrams, grams, and so forth and this gives you you the size of time the substance has been decaying.

Answer 3

P = P(0) e^.047t

P = P(0)[1.047]^t