Question

16.) A. B. C. Algebra 2 chapter 7

Answer 1

Your equation for exponential growth is of the form $y=a(b) ^{x}$, where a is the initial or starting value and b is the multiplier.  DO NOT EVER EVER MULTIPLY A TIMES B AND THEN RAISE IT TO THE X POWER! This is not the way you do these.  A and B remain separate.  In our situation, we have an equation that looks like this $y=8(4) ^{x}$.  That's part a.  Now we need to find how many bacteria are on it 5 hours later, which will be subbed in for our x in the equation.  $y=8(4) ^{5}$.  Raise 4 to the 5th power first to get 1024, then multiply that by 8 to get a total of 8192 bacteria on your cookie 5 hours later.  That's part b.  Now for part c, you're going to have to use some of the properties of logs to solve this.  This time they're asking for the time it takes to get 100,000 bacteria on the cookie, which is your x value.  You need to get it out from being an exponent to being a "regular" variable we can solve for.  So our equation now uses the number of bacteria as our y: $100,000=8(4) ^{x}$.  Begin by dividing both sides by 8 to get rid of it on the right: $12,500=4 ^{x}$.  Now take the log of both sides to bring down that x: $log(12,500)=log(4) ^{x}$, and using the power property we have log(12,500) = x log(4).  Now we will divide both sides by log(4) to isolate the x and do the work on our calculator to find that x= 6.80.  In other words, it will take just short of 7 hours for your cookie to have 100,000 bacteria on it.  I'd suggest cafeteria food, but that might kill you quicker!