Answer:
Step-by-step explanation:
This is of the form
Where P(t) is the ending population, a is the original population, b is the growth rate, and t is time in years. We have everything we need to solve for t.
Let me explain the growth rate quickly. If the exponential function is a growth function, that means (in this particular situation) that we have 100% of the population and we are increasing it by 19%. That makes the growth rate 119%, which in decimal form is 1.19.
Begin by dividing both sides by 40000 to get
To get that t out of its current exponential position, take the natural log of both sides:
and the rules of logs say we can bring the exponent down out front:
ln(2) = t*ln(1.19)
Divide both sides by ln(1.19) to get t alone:
Doing that calculation on your calculator gives you that
t = 3.9846...
but rounding to the nearest tenth gives you that
t = 4.0 years
Well since you dont have the graphs posted i can tell u the y-intercept and the slope and you can figure it out from there.
8x-y=-4
-y=-8x-4
y=8x+4
the y intercept is 4 and the slope is positive 8
Factor by grouping. Group up the terms into pairs, factor each pair, then factor out the overall GCF.
x^3 + 2x^2 - 16x - 32
(x^3 + 2x^2) + (-16x-32) ... pair up terms
x^2(x + 2) + (-16x - 32) ... factor x^2 from the first group
x^2(x + 2) - 16(x + 2) ... factor -16 from the second group
(x^2 - 16)(x + 2) .... factor out (x+2)
(x - 4)(x + 4)(x + 2) .... Use the difference of squares to factor x^2-16
---------------------------
The original expression completely factors to (x - 4)(x + 4)(x + 2)
The three factors are x - 4 and x + 4 and x + 2
To determine the probability that one or the other circumstances will occur, you will count the number of possible outcomes and divide it by all the possible outcomes.
#of female teaching assistants + # of male teaching assistants + # of female professors
6 + 16 + 11 = 33
Total = 41
33/41 = 80
There is a approximate 80% probability that one or the other will occur.
