Question

In a country, the annual food production is 50000 units and the population is 50000 in the first year. Assume that the food production increases by 5000 units per year and the growth rate of the population is 5% each year.
(a) (i) Find the food production in the 5th year. [Done; 70000units]
(ii) Find the population in the 5th year. [Done; 60800]
>>>>(b) If the annual food production stops increasing after five years, when will the annual food production be less than the population?<<<<
>>>>(c) When the ratio of food production to population is less than 1:5, there will be a food shortage. Estimate if there is a food shortage at the end of the 50th year.<<<<

@terenzreignz @Callisto @hartnn @mathslover

Answer 1

food production follows an arithmetic progression, food production follows a geometric progression.

Answer 2

<Part b>
Since the annual food production stops increasing after five years, the annual food production will remain constant after 5 year, what is that constant?

Answer 3

@Callisto : 70000 units???

Answer 4

Yes. And we need to find "the annual food production be less than the population"
You know the annual production, which is a constant, less than is just an inequality sign. You also know the formula to find the population. You can set an inequality and solve it.
What is the inequality?

Answer 5

70000 < 50000*(1+5%)^(n-1)
??

Answer 6

Yes. Now, you can solve the inequality!

Answer 7

but i cannot solve it

Answer 8

7/5 < (1+5%)^(n-1)

Answer 9

take log?

Answer 10

Yes, take log.

Answer 11

ohh...wait

Answer 12

\[\frac{ \log \frac{ 7 }{ 5 } }{ \log(1+0.05) }>n-1\]

Answer 13

\[n \approx8 ??\]

Answer 14

Why did you change the sign?

Answer 15

log...

Answer 16

OMG, sorry, my fault.
<

Answer 17

Looks good now :)

Answer 18

and part c?

Answer 19

@Callisto

Answer 20

What is the food production and population in the 50th year?

Answer 21

FP: 50000+(50-1)*5000=295000
P: 50000*(1+5%)^(50-1)=546066.6565

is it?