1. The annual revenue for Amazon.com rose from approximately...

1. The annual revenue for Amazon.com rose from approximately $10.7 billion in 2006 to $74.5 billion in 2013. a. Use this information to build an exponential model for Amazon's annual revenue I, in billions of dollars, as a function of time t in years since 2005. (Round A and b to three significant figures when reporting your answer but store the full values in your calculator.) b. Use the model to predict the 2015 revenue. Use the stored values to make the prediction. 2. Find the equation of the exponential function that passes through the points (1, 1.2) and (2, 0.24).

Transcript

00:01 In the given question we are told that the annual revenue for a certain website rose from approximately 10 .7 billion in 2006 to 74 .5 billion in 2013.

00:16 The first part of the question is to build an exponential model for this annual revenue and we are told to take the annual revenue as i would use as.

00:30 The annual revenue and we are told that this should be taken as a function of time t in years since 2005.

00:45 So what we could do then is we can just simply write an exponential equation of the form a times b to the power of t where t is the time in years.

01:00 Time in years since in years since 2005 so now we can see that i is equal to 10 .7 billion 10 .7 when t is equal to 1 that is in the year 2006 so a 8 times b to the power of 1 given gives us 10 .7 which means a times b gives us 10 .7 and now when we take t equal to in 2013 which is eight years from 2005 that is when t is equal to eight i is equal to uh 74 .5 billion and this is a a times b to the power of eight so first what we can do over here is we can take this as equation number one and this as equation number two and we are going to divide equation number two with equation number one so we will have 74 .5 divided by 10 .7 is equal to a times b to the power of eight divided by a times b uh a divides b raised to the power of 8 divided by b is b raised to the power 7 and this is equal to 74 .5 divided by 10 .7 from which we can write b is then equal to 74 .5 divided by 10 .7 raised to the power of 1 by 7 so now when we take 74 .5 divide it with 10 .7 and take the power of this value as 1 by 7 what we would get as the value of b over here is 1 .3194 3194 6 so now that we have the value of b we can find the value of a by substituting the value of b in equation number 1 so we will have 10 .7 is equal to a times b where b is equal to 1 .3190.

03:31 946.

03:33 So from this we can write a is then equal to 10 .7 divided by 1 .3946 and on dividing 10 .7 with 1 .31946, we get the value of a to be equal to 8 .1 .8 .109 which we can approximate as 8 .11.

03:59 So now that we have the values of a and be the exponential model that we had to find is i equals 8 .11 times 1 .31946 raised to the power of t so now that we have found the exponential model the next thing that we have to find is to predict the revenue in 2015 using this model so 2015 means the t that is the time in years since 2005 is 10 so when t is equal to 10 the annual revenue would be 8 .11 times 1 .31946 raised to the power of 10 and when we take the power of 1 .31946 as 10 and multiply this with 8 .946 what we would get as the revenue the annual revenue in 2015 is a hundred and twenty nine point six nine six eight billion which we can approximate as a hundred and twenty nine point a hundred and twenty nine point seven billion right so this is the revenue in the year two thousand and fourteen now the next question is different from the one that we have already solved...

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