Question

one model of earth population growth is p(t) equals 64/1 plus 11e^-.08t
Will medal

Answer 1

oooooooooook. noted

Answer 2

Any question?

Answer 3

another model of earht is Heidi Klum btw
now, she doesn't have any exponents, but she does decently in her job

Answer 4

earth even

Answer 5

XD

Answer 6

@John_ES One model of earth population growth is p(t)=64/(1+11e^-.08t) where t is measured in the years since 1990, and p is measured in billions of people.
which of the following statements are true?
A:The population of Earth will grow exponentially for a while but then start to decrease
B: In 1991 there were 5.74 people according to this model
C: The carrying capacity of Earth is 64 billion people
D: The population of Earth is growing at a rate of just under 8% per year

Answer 7

Well, watching the function you see that
\[t\rightarrow \infty \Rightarrow p(t)\rightarrow 64\] Ok?

Answer 8

So the first question cannot be true. There is no exponential decay, just the model says the population will reach a constant value. Ok?

Answer 9

Okie

Answer 10

For the second, as t is measured in years taking the zero at 1990, you must evaluete the function for t=1,
\[p(1)=\frac{64}{1+11e^{-0.08\cdot1}}\]

Answer 11

What do you obtain?

Answer 12

74.15

Answer 13

So, not true then?

Answer 14

Not exactly, the value is 5.7377 that is 5.74, so it is true.

Answer 15

Oh, I didn't put parentheses around the bottom one.

Answer 16

For the C question, we know from the A question that the there is a constant limit value whose value is 64. So, it is true too.

Answer 17

Okie

Answer 18

Now, the last question. They ask for the growing rate, so we must calculate the rate. To do it you must do the following:
\[p(2)-p(1)\]
This gives you the growth in one year. They gives a number in %, so you must compare with the original and multipliy by 100:
\[\frac{p(2)-p(1)}{p(1)}\cdot1000\] Try to calculate and tell me your result.

Answer 19

Sorry, it is not a 1000 is a 100

Answer 20

I'm really confused

Answer 21

Ok, for the growth is just calculate the growth with the formula they provide,
\[p(1)=5.74\] the previous result,
And \[p(2)=6.17\]Ok?

Answer 22

So it would be just under 8%

Answer 23

So the population increase in
\[p(2)-p(1)=0.43\]
Now you want to calculate which percentage represents this number, so
\[\frac{0.43}{p(1)}\cdot 100=7.52\approx 8\%\] So it is true.

Answer 24

So, B: In 1991 there were 5.74 people according to this model, C: The carrying capacity of Earth is 64 billion people & D: The population of Earth is growing at a rate of just under 8% per year are all correct, right?

Answer 25

Correct!

Answer 26

Thank you!