Translate the following statements into algebraic relations of the form Y’ = fY

Question

Translate the following statements into algebraic relations of the form Y’ = fY where Y’ is the current quantity, Y is the previous value of the quantity and f is the factor by which Y should be multiplied to give Y’. In so doing, determine the factor f . The key will be available on blackboard, usually within an hour or two after discussion ends. To avoid

1.Mary’s speed is 2.8 times as fast as Jeff’s speed. Use ‘v’ to represent speed?

2.The leaky container has 25% less fluid in it today than yesterday. (Let’s describe the amount as a volume and use V to represent volume).

3.The population of New York City grew by 0.85% in 2012 compared to 2011.

4.The length of both sides of a rectangle increased by a factor of 1.5. Write a relation for the increase in the area of the rectangle. Let A represent area

5.the volume of a sphere increases by a factor of 17. By what factor did its radius increase?

Explanation / Answer

1) let Jeff's speed be =v

so, Mary's speed = 2.8v

( Mary's speed will be as Y' and f will be factor of 2.8 and Y is Jeff's speed)

2) let previous value is V of the container before any leakage so , current value after 25% leakage

V'=0.75 V

(V': current volume and V= previous)

3) population in 2011= P( say)

current population P'=(100+0.85)/100*P

P'=1.0085P

4) let the are be A=l*b

when both l and b are increased by a factor 1.5 so A'=1.5l*1.5b =2.25 l*b

new area is A' previous area is A

so A'=2.25 A

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