One model of Earth's population growth is P(t)=64÷(1+11e^(-.08t)), where t is measured in years since 1990, and P is measured in billions of people. Which of the following statements are true? Check all that apply.

A. The population of Earth is growing at a rate of just under 8% per year.
B. In 1991, there were 5.74 billion people, according to this model.
C. The carrying capacity of Earth is 64 billion people.
D. The population of Earth will grow exponentially for a while but then start to decrease.

Question

One model of Earth's population growth is P(t)=64÷(1+11e^(-.08t)), where t is measured in years since 1990, and P is measured in billions of people. Which of the following statements are true? Check all that apply.

A. The population of Earth is growing at a rate of just under 8% per year.
B. In 1991, there were 5.74 billion people, according to this model.
C. The carrying capacity of Earth is 64 billion people.
D. The population of Earth will grow exponentially for a while but then start to decrease.

anonymous · Answer

@campbell_st  no idea?

campbell_st · Answer

well the equation doesn't make a lot of sense to me... if I read it correctly

its 

$$P(t) = \frac{(1 + \frac{11}{e^{0.08t}})}{64}$$

anonymous · Answer

it looks like this..

campbell_st · Answer

which seems to indicate exponential decay... rather than growth

campbell_st · Answer

ok... oops... my mistake... 

so t = 1

anonymous · Answer

Im thinking C is a possible answer but I need at least one more  answer

campbell_st · Answer

ok... so looking at it.

B is correct... when I substituted t = 1   (representing 1 year since 1990) 

I got a population P(1) = 5.73771 billion people

anonymous · Answer

population being 5.7 would make C wrong then?

campbell_st · Answer

I graphed the curve and D seems to make sense

anonymous · Answer

so it'll end up being 
B and D ?

campbell_st · Answer

the graph flattens out at 64 billion... 

this is because as t approaches infinity.... e^(-0.08t) approaches zero... 

so 11*(e^(-0.08t) will approach zero leaving

64/1 = 64... 

so C seems right...

anonymous · Answer

hmmm so what would be the final two answers or are you pretty sure B, C and D make sense ?

campbell_st · Answer

looking at A

then t = 0.. the population is 64/12 = 5.333... billion

then 1.08 x 5.3333 = 5.76... so 1991 or P(1) is approx 5.76... close

then looking at 1991 to 1992

P(1) = 5.74   P(2) = 6.17

so to check 

5.74 x 1.08 = 6.199

so it appears the growth rate is approx 8%...

campbell_st · Answer

so for me... I'd probably check A to C.

 and  D the population won't decrease... just gets to a max value... 

so I'd leave that out... after looking at it again

campbell_st · Answer

hope it all helps

anonymous · Answer

thank you!:) @campbell_st

campbell_st · Answer

glad to help.... and I hope it was correct...