Please see the attached. (a) A town has a population of 5000 persons, but is expected to grow by 2% every year.(i) What would be the population size in 7 years?(ii) Find the sum of the first eight terms of the sequence1 1 14 '2(b) A landscape contractor is hired to cultivate ornamental plants in three new residentialdevelopments. The contractor charges the developer for each tree cultivated, an hourly rateto cultivate the ornamental plants, and a fixed delivery charge. In one development it took211 labour hours to cultivate 244 ornamental plants for a cost of $9394. In a second developmentit took 128 labour hours to cultivate 283 ornamental plants for a cost of $8270. In the finaldevelopment it took 165 labour hours to cultivate 386 ornamental plants for a cost of $10938.

Name: Please see the attached. (a) A town has a population of 5000 persons,
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Description: Please see the attached. (a) A town has a population of 5000 persons, but is expected to grow by 2% every year.(i) What would be the population size in 7 years?(ii) Find the sum of the first eight terms of the sequence1 1 14 '2(b) A landscape contrac

Answered: (a) A town has a population of 5000…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Please see the attached.

(a) A town has a population of 5000 persons, but is expected to grow by 2% every year.
(i) What would be the population size in 7 years?
(ii) Find the sum of the first eight terms of the sequence
1 1 1
4 '2
(b) A landscape contractor is hired to cultivate ornamental plants in three new residential
developments. The contractor charges the developer for each tree cultivated, an hourly rate
to cultivate the ornamental plants, and a fixed delivery charge. In one development it took
211 labour hours to cultivate 244 ornamental plants for a cost of $9394. In a second development
it took 128 labour hours to cultivate 283 ornamental plants for a cost of $8270. In the final
development it took 165 labour hours to cultivate 386 ornamental plants for a cost of $10938.

Expert Solution

Step 1

Note: We are allowed to answer first part only. Also the question in second part is not complete. Please resubmit the rest parts with all necessary details.

$(a)$

Given:

Population of a town= $500 p e r s o n s$

It is expected to grow by $2 %$ every years.

We have to find population size in 7 years.

Step 2

$(i)$ As the population is growing every year by $2 %$ .

The initial population $= 5000$

Then the population in $7$ years is:

$(5000) {(1 + \frac{2}{100})}^{7} = 5000 \times {(1 + 0.02)}^{7} = 5000 \times {(1.02)}^{7} = 5, 743.42835 \approx 5744 p e r s o n s$

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