Maths please someone help me out!!!
posted by Jasmine .
3. The efficiency of an industrial pump decreases by a fixed percentage each year. The percentage decrease each year is with respect to the efficiency of the pump at the start of each year. Over each four year period, the efficiency decreases by 80%. Let us write e = f(t) so that the efficiency e of the pump, as a percentage of itâ€™s initial efficiency, is a function of the number of years t since the pump has been in operation.
(a) Make a table of values of the function for changes in t of 4, starting from t = 0.
(b) Explain why the formula is given by e = f(t) = 100(0.2)t/4.
(c) By a process of guessing, checking and fixing (no logarithms yet!) estimate the time taken for the efficiency to reach 50%. Choose a reasonable level of accuracy.
(d) Show that the halving time is in fact constant by showing that no matter what time we consider, say t = a, if you then add the time found in the previous part, the efficiency is halved.
(e) Use the halving time to make a sketch of the function over an 8 year period.

.2^(t/4) multiplies by 0.2 every time t increases by 4. That's how the efficiency is described in words.
so, get out your calculator (online or physical) and evaluate some values for t. As a sanity check, 50% is a little more than twice as much as 20%, so expect t to be somewhere around half of the 4year cycle.
Respond to this Question
Similar Questions

Pump power
I have a question in a tutorial, one of these that give the answers in brackets. However, I think the answer given may be wrong. Anyone check this please, if the given answer is correct, how is it worked out. Q A centrifugal pump is … 
Physical Science
When you do 100 J of work on the handle of a bicycle pump, the pump does 40 J of work pushing the air into the tire. What is the efficiency of the pump? 
physics
The efficiency of a machine is in general defined as the ratio between useful (released) energy and the input energy. Therefore, the exact formulas for efficiency depend on the purpose of the machine. What's the difference in the maximal … 
Maths algebra
The efficiency of an industrial pump decreases by a fixed percentage each year. The percentage decrease each year is with respect to the efficiency of the pump at the start of each year. Over each four year period, the efficiency decreases … 
Physics
A piston in a bicycle pump is pressured half way into the pump without letting air get out and at unchanged temperature. Inside diameter of the pump is 2,3 cm. a) What is the pressure inside the pump in atm? 
Hydraulics
A centrifugal pump impeller has an outside diameter of 290mm and the with at the outlet is 110mm. The vanes are set back at an angle of 35 degrees to the tangent to the impeller at the vane tip. The diameter of the suction and delivery … 
Hydraulic machines
A centrifugal pump impeller has an outside diameter of 290mm and the with at the outlet is 110mm. The vanes are set back at an angle of 35 degrees to the tangent to the impeller at the vane tip. The diameter of the suction and delivery … 
Math
A car decreases in value by 20% for the first year, and for each later year by 12% of its value at the beginning of that year. Calculate the percentage decrease in the value of the car after 3 years. Answer not 44% if that is what … 
Science
A pump is used to lift 500 kg of water from a depth of 80 m in 10 seconds.Calculate the power rating of the pump if it's efficiency is 40% . Take g=10 m/ s*s. 
Maths
A car depreciates in value by 15% for the first year and for each year later by 12% of its value at the beginning of that year. Calculate the percentage decrease in the value of the car after 3 years. Could someone please confirm the …