Maths-
General
Easy
Question
The wholesale price of a kilogram of lentils decreased by 1% from the previous month for six consecutive months. If x is the number of months since the price began to drop and y is the cost of a kilogram of lentils, which of the following equations could model the cost of lentils over this time period?
- y = 0.99x + 1.65
- 1.01x + 1.65
- 1.65 (0.99)x
- 1.65 (1.01)x
Hint:
1.65(0.99)x
The correct answer is: 1.65 (0.99)x
Hint:
Exponential decrease means when there is an decrease in initial number by the same percentage/ factor over equal time intervals. This can be represented in mathematical form as follows-
where-
a = Initial number
r = rate of decrease
t = time during which the decrease occurred
Step-by-step solution:-
Since in the given question, the price of lentils decreases by a constant rate of 1% every year for 6 consecutive months, it is an example of exponential decrease.
∴ applying the above function where-
f (x) = function modelling the price of lentils = y
a = Initial cost
r = rate of decrease every month = 1%
t = time during which the cost decreased = x
∴ y = a (0.99)x --------------------- (Equation i)
The only option in the given question that matches with Equation i is Option C.
Final Answer:
Option C i.e. y = 1.65 (0.99)x is the correct Option.
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