SOLUTION: Please help me to solve this question. Question 1 Suppose a certain population grows according to the formula N = NoE^kt, where N is number of people (in millions) at time t (

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Question 1042662: Please help me to solve this question.
Question 1
Suppose a certain population grows according to the formula N = NoE^kt, where N is number of people (in millions) at time t (in years), No is the number of people (in millions) when an observation was first made, and k is a constant. Suppose the population increases from 2 million to 32 million in 80 years.
1.1 Use the given formula to determine the constant k (leave your answer in ln, if necessary).
1.2 Calculate the time in which the population will double.

Question 2
Suppose that an amount of $5000 is invested for 3 years, and the interest is compounded monthly at an annual rate of 10%. Write down a formula, simplified as far as possible, to represent the amount that the investment will be worth after 3 years.
Do not calculate the answer.

Thank for your help...
Found 3 solutions by Boreal, josgarithmetic, MathTherapy:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
n=Noe^kt
80,000,000=2,000,000e^k*80
divide by 2000000
40=e^80t
ln of both sides
ln 40=80t
t=ln 40/80
-----------
doubling, n=2No
2No=Noe^kt
2=e^(ln40/80)*t
ln 2=[ln (40)/80]t
divide both sides by ln (40)/80. That inverts the denominator.
80[ln 2/ln40]=t
========
A=Ao{1+r/n}^nt
=5000{1+.10/12}^36
=5000(1.08333}^36
the exact answer is 5000{12.1/12)^36

Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Question 1 looks like exponential growth, but you might want instead of the unknown E base, to use a more typical e base, approximately or close to 2.71828 something. Write a better shown equation format N=N%5Bo%5De%5E%28kt%29.

Your given data is population goes from 2 million to 32 million in 80 years.
Question first asks, find k.

ln%28N%29=ln%28N%5Bo%5D%29%2Bln%28e%5E%28kt%29%29
ln%28N%29=ln%28N%5Bo%5D%29%2Bkt%2Aln%28e%29
kt%2Bln%28N%5Bo%5D%29=ln%28N%29
highlight%28kt=ln%28N%29-ln%28N%5Bo%5D%29%29 OR highlight%28kt=ln%28N%2FN%5Bo%5D%29%29
and you can use either of these to find a formula for k or for t.

TO get the value of k in question 1, make these substitutions after solving the formula for k:
system%28N=32%2CN%5Bo%5D=2%2Ct=80%29.

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!
Please help me to solve this question.
Question 1
Suppose a certain population grows according to the formula N = NoE^kt, where N is number of people (in millions) at time t (in years), No is the number of people (in millions) when an observation was first made, and k is a constant. Suppose the population increases from 2 million to 32 million in 80 years.
1.1 Use the given formula to determine the constant k (leave your answer in ln, if necessary).
1.2 Calculate the time in which the population will double.

Question 2
Suppose that an amount of $5000 is invested for 3 years, and the interest is compounded monthly at an annual rate of 10%. Write down a formula, simplified as far as possible, to represent the amount that the investment will be worth after 3 years.
Do not calculate the answer.

Thank for your help...
highlight_green%28k+=+%28ln+%2816%29%29%2F80%29

Population doubles in highlight_green%28matrix%281%2C2%2C+20%2C+years%29%29