Question

One model of Earth's population growth is

Here's a picture http://media.apexlearning.com/Math/200706/06/38abe12b-e995-42fa-932c-e5e200104cd7.gif

A. The population of Earth will grow exponentially for a while but then start to slow down its growth.
B. In 1990, there were 5.33 billion people.
C. The carrying capacity of Earth is 5.33 billion people.
D. The population of Earth is increasing by a steady rate of 8% per year.

I'm thinking the answer's are A and B but I'm not sure! please help me understand

Answer 1

We can have multiple correct answers on this one?

Answer 2

yes!

Answer 3

You can work out B and C right?

Answer 4

im not sure

Answer 5

it could also be answer D. im confused

Answer 6

Set t= 1990 and work out the value of population. If it is 5.33 billion then b is correct

Answer 7

Wait a minute is the value of t is going to directly have the numerical value of year or is it going to go through some process?

Answer 8

Can you send the whole question if possible?

Answer 9

I'm so sorry I forgot there was more to this question!

measured in years since 1990, and P is measured in billions of people. Which of the following statements are true

Answer 10

Okay so set the value of t = 0 and then work out the value of function. If the answer is 5.33 then B is correct

Answer 11

which other answer is correct?

Answer 12

Can C be correct?

Answer 13

im not sure lol this is so hard for me

Answer 14

The carrying capacity of Earth is 5.33 billion people. Set an equality
\[\large\rm \frac{64}{1+11e^{0.08t}} >5.33\]
Work ou the value of t. If it is positive then the statement is true.

Answer 15

i got t<0.00852515 is that positive?

Answer 16

(b) and (c)
for b: set t=0 (year 1990) you will get 5.33 (pop in billions in 1990)
for c: for rel. small t the exp function dominates the denominator. Since it has negative power you can view it as exponential in the numerator and hence the growth can be called approximately exponential. As t gets larger this this trend attenuates and the growth becomes flat. (whic, btw., makes the statement (d) incorrect!)

Answer 17

so b and c are the correct answers?

Answer 18

@FaiqRaees

Answer 19

Are you sure you solved the equation correctly?

Answer 20

probably not :( ugggggh sorry for being difficult

Answer 21

Well then c is correct

Answer 22

B and C are correct....

Answer 23

D is wrong since its a curve so a constant gradient/ slope cant be achieved since rate refers to gradient

Answer 24

For A equate the derivative to 0, if equation satisfies than a is also correct

Answer 25

i dont think A is correct

Answer 26

so b and c?

Answer 27

Yeah