Example
The value of a Samsung Galaxy S4 is $600. The value of the phone decreases 5% per year.
a) Write an exponential equation. Use y for the value of S4, and x for the number of years.
b) What will the S4 be worth in 10 years? (Round to the nearest cent)
c) When will the S4 be worth $541.50? (Round to the nearest cent)
Solution
a) As part (a) says, we write an exponential equation by using x and y:
In 10 years, the S4 will be $359.24
In 2 years, the S4 will be $541.50.
EQUATION, TABLE, AND GRAPH
reflection
In this example, what we are trying to find is finding the price of a Samsung Galaxy S4 whose value decreases 5% every year. This problem is an example of percent decrease. To find the price we have to use an exponential equation which is y=a*(b-c)^x. To calculate percentage decrease: First: work out the difference (decrease) between the two numbers you are comparing. Then: divide the decrease by the original number and multiply the answer by 100. If your answer is a negative number then this is a percentage increase. The variables that represents the price is 'y' and the variable that represents the number of years is 'x'. Example being for 10 years, you substitute 'x' with 10 and solve from there and you get $359.24. The word problem is more of the simpler problems that involves percent decrease. Being very straight forward since at this point you have learned exponential growth which follows the same principle. Overall this problem is decently simple.