Big Ideas Math Integrated I, 2016
BI
Big Ideas Math Integrated I, 2016 View details
4. Solving Exponential Equations
Continue to next subchapter

Exercise 50 Page 304

Practice makes perfect
a

To find when the events will have the same attendance, we want to find the x-value when the two functions intersect.

We can see that the functions will intersect around x=3. Note that year 0 corresponds with 2004. This tells us that x=3 is really the year 2007, so in approximately 2007 the attendances should be equal.

b
We can verify this by checking if the functions are actually equal at x=3. Since we are given the equations, we will substitute x=3 into the equations and see if they are equal.
4000(1.25)^x=12 000(0.87)^x
4000(1.25)^3? =12 000(0.87)^3
1.25^3? =3(0.87)^3
1.95? =3(0.66)
1.95? =1.98
We can see that while x=3 is not the exact answer, it is certainly a very close approximation.