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Mathematics>Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer.

The number of data objects stored in a company's "cloud" increased at a rate of 190% per year for 5 years. At the end of the fifth year, the number reached 762 billion objects. From the beginning of the sixth year, 1 billion objects were being added daily to the company's cloud. If the growth rate had not changed in the sixth year, approximately how many more objects would have been on the company's cloud at the end of the sixth year than the actual number of objects based on the constant daily increase? (Use 365 days per year.)

A.1.1 trillion objects
B.2.2 trillion objects
C.320 billion objects
D.397 billion objects

答案和解析

答案：B

解析：

Choice A is correct. If the number of objects was growing by 190% per year, that meant there were 100%+190%=290% as many objects at the end of one year as there were at the end of the previous year. That is the same as multiplying by 2.9 each year. The growth during the first 5 years can be modeled using the expression A*2.9^t, where A is the initial number of objects stored in the cloud and t is the number of years that have passed.

Since there were 762 billion objects at the end of the fifth year, if the number of objects continued to grow at the same rate, by the end of sixth year this number would be 2209.8 billion, which is about 2.2 trillion.

Once the company begins reporting a steady amount of increase per day, we can use a linear model. Since during the sixth year, 1 billion objects were added each day, 365 billion objects were reported to be added in the sixth year. So the total number of objects (in billions) at the end of the sixth year is 762 +365=1127, or approximately 1.1 trillion objects.

Therefore the difference between the total number of objects that would have been stored if the rate remained exponential and the total number of objects given the linear rate (in trillions) is 2.2-1.1=1.1. So, there would have been about 1.1 trillion more objects stored if the rate continued to be exponential.