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(a) A town has a population of 5000 persons, but is expected to grow by 2% every yea (1) What would be the population size in 7 years? 1 1 1 2' 3די8 (ii) Find the sum of the first eight terms of the sequence -- ......

(a) A town has a population of 5000 persons, but is expected to grow by 2% every yea (1) What would be the population size in 7 years? 1 1 1 2' 3די8 (ii) Find the sum of the first eight terms of the sequence -- ......

Advanced Engineering Mathematics
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 disregard the last 2 questions...

Please see the the question below.

(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? 1 1 1 4'2 (ii) Find the sum of the first eight terms of the sequence (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 rat 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 develo 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 $109 In total 504 labour hours were taken and 913 ornamental plants were cultivated. Using Cramer's Rule of the Inverse Method, determine the cost for each tree, the hourly labour charge, and the delivery charge.
Transcribed Image Text:(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? 1 1 1 4'2 (ii) Find the sum of the first eight terms of the sequence (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 rat 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 develo 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 $109 In total 504 labour hours were taken and 913 ornamental plants were cultivated. Using Cramer's Rule of the Inverse Method, determine the cost for each tree, the hourly labour charge, and the delivery charge.
Expert Solution
Step 1

Given,

Initial population of a town is 5000 persons.

It is given that it increases at a rate of 2% every year.

Here we shall use the exponential growth formula.

P=P01+rt

Here P is the final population, P0 is initial population, r is the rate of growth and t is time in years.

 

Step 2

Now we shall plug the values in formula we get,

P=50001+0.027P=50001.027P=5743.42

Hence after 7 years population shall be 5743.

 

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