Question

the population of a country is currently at 56 million and is forecast to rise by 3.7 % each year. it is capable of producing 2500 million units of food each year, and it is estimated that each member of the population requires a minimum of 65 unit of food each year. at the moment , the extra food needed to satisfy this requirement is imported , but the government decides to increase food production at a constant rate each year , with the aim of making the country self sufficient after 10 years. find the annual rate of growth requied to achieve this.

Answer 1

First, write the equation for population growth.

Answer 2

56(1+3.7/100) ?

Answer 3

It should be (population)1.037

Answer 4

37 % the population right ?

Answer 5

It's the same as what you said, but accounts for the varying pop. It's 103.7% --> 1.037

Answer 6

Now, find what the population will be in 10 years.

Answer 7

what about food?

Answer 8

56(1+3.7/100)^10

Answer 9

Since we want to find out how much food we'll need in 10 years, we need to know how many people there will be in 10 years.

Answer 10

56(1+3.7/100)^10=86.60 right>

Answer 11

is it right?

Answer 12

for 56(1+3.7/100)=58

Answer 13

I got 80.5

Answer 14

yea you have right !

Answer 15

Okay, so we have 80.5 million people in 10 years. How much food will they need to eat?

Answer 16

minimum required of 65 unit for food each year and it is capaple to producing 2500 million unit of food

Answer 17

65 unit for food each year per person right? So what will we do to find the total amount?

Answer 18

exactly

Answer 19

the anwer we find divide by the food per person?

Answer 20

Actually, we will multiply so there will be 65 units for each of the millions of people.

Answer 21

80.5 mutiplie by 65?

Answer 22

Remember It's not just 80.5, it's 80.5 million.

Answer 23

yea i know but the anwser will in million but is correct that i shoudl 80.5 multiplie by 65=5232.5 million ?

Answer 24

yep!

Answer 25

we need annual rate of growth required

Answer 26

We know how much we need, so now we need a function that will get us from the current annual growth rate to 5232.5 million food units.

Answer 27

so 5232.5( 1+r/100)?

Answer 28

Not exactly. 5232.5 is the result we already have. It's where we need to get to.
It will be to the right of the "=".

Answer 29

What's the current annual food production?

Answer 30

each year annual food

Answer 31

yes. What is the food production currently?

Answer 32

they can produce 2500 million unit of food

Answer 33

Right, now what will get that equal to 5232.5 in ten years?

Answer 34

here i dont know ^^

Answer 35

It's the compound interest formula. What's the beginning amount you have?

Answer 36

56million rise 3.7 % i know it is compound interest formula but how i can do for food if i dont have rate

Answer 37

ah maybe because food per populatioN

Answer 38

EXACTLY! You don't have the food rate. When you don't know what something is, we call it a variable x

Answer 39

so 2500(1+r/100) then we can do for 10 year?

Answer 40

Right. What do you do with the ten? Don't forget to set it equal to 5232.5.

Answer 41

ahh kk so 2500(1+r/100)^10=5232.5

Answer 42

Yep, that's the equation!

Answer 43

You just need to solve for r.

Answer 44

so then 5232.5 /2500=(1+r/100)^10
ln(5232.5/2500)=10ln(1+r/100)
ln(5232.5/2500)/10=ln(1+r/100_
i do expenential? for both

Answer 45

then x anwser-1multiplied 100= r?

Answer 46

Get rid of the 2500 first. Then take log 10 of both sides. What does that give you?

Answer 47

i found the final anwser 7.66 %

Answer 48

is it correct?

Answer 49

Yes!

Answer 50

Good job!

Answer 51

THANK YOU :D awnsome how i can give you medal? i am new here ^^

Answer 52

You click "Best Response". No problem.

Answer 53

It should be right next to the medal on one of my responses.