Exponential Word Problem help?

label Mathematics
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schedule 1 Day
account_balance_wallet $5

Julia and her brother, Emilio, are both saving to buy a new computer that costs $1,000. Julia is saving $100 a week and her brother is saving at a weekly rate of 10x-2, if x = the number of weeks of saving. Which of them will reach their $1000 goal first? Explain your answer.

Apr 6th, 2015

If Julia is saving at a rate of $100 a week, and x = the number of weeks of savings, then to determine when she will have a $1000, the equation would be:

100x = 1000

x = 10   which means that Julia will reach her goal of $1000 in 10 weeks

Now let's look at Emilio.  His weekly rate of savings is given by

10x - 2

Then to determine how many weeks it will take him to reach his goal, we set up the equation like this:

10x - 2 = 1000

Now we solve for x:

10x = 1002

x = 100.2 weeks

So, Julia will reach her goal MUCH faster than Emilio.

Apr 6th, 2015
Thank you for answering but I made a typo, Emilio's weekly rate is actually 10^x-2 not 10x-2.
Apr 6th, 2015

OHHHH.... that makes a world of difference :)

Then, for Emilio it would be

10^x-2 = 1000

Now take the LOG of both sides to get

log(10^x-2) = log(1000)

x - 2 = 3

x = 5

So, Emilio is the WINNER!!  It only takes him 5 weeks to reach the goal.

Apr 6th, 2015

That makes a lot of sense! Thank you so much! 

Apr 6th, 2015

You're welcome :)

Apr 6th, 2015

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