AAR- Unit 5 Day 3 Solving Exponential Word Problems

AAR- Unit 5 Day 3 Solving Expo Word Problems

by Kelcey Cook

Multiple Choice

Ash has $8,000 in a savings account. The interest rate is 3% compounded once a year.

What is the equation for this situation?

• $$y=8000\left(3\right)^x$$

• $$y=.03\left(8000\right)^x$$

• $$y=8000\left(1.03\right)^x$$

• $$y=8000\left(1.3\right)^x$$

Multiple Choice

A sailboat that costs $5,950 decreases in value by 11% per year. What is the equation that represents this?

• $$y=5950\left(.89\right)^x$$

• $$y=5950\left(.11\right)^x$$

• $$y=5950\left(1.11\right)^x$$

• $$y=11\left(5950\right)^x$$

Multiple Choice

Does the following equation show growth or decay?

y=10000(0.76)^x

• Growth 
• Decay

Multiple Choice

An air freshener starts with 30 grams of fluid, and the amount of fluid decreases by 12% per day.

• Q=30(1+0.12)^t

• Q=30(-0.12)^t

• Q=30(0.88)^t

• Q=12(1.30)^t

Fill in the Blanks

P = 8(1.23)^t

What is the initial quantity?

Multiple Choice

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

• y = 15(35)^x

• y = 15(0.35)^x

• y = 15(1.35)^x

• y = 35(1.15)^x

Multiple Choice

Make the percent to decimal.
7.25%

• 7.25
• 72.5
• 0.725
• 0.0725

​In order to solve an exponential word problem, you need to know if you are given an x-value or y-value in the problem!

X MEANS TIME!

​*THESE QUESTIONS WILL ASK YOU TO FIND HOW MANY!

​

​*Watch for years! If the year in the problem is 2003, and the problem asks you to find the number of people in a town after 7 years. Your x value would be ____________!

​

​*If it says the population was 45 in 1980 and increased by 6%. What is the population in 2012. You would plug in __________.

Y MEANS A TOTAL!

​*THESE QUESTIONS WILL ASK YOU TO FIND WHEN!

​

​*EXAMPLE: Find when the population will reach 1000

​*EXAMPLE: Find when the account balance will reach $50000

Multiple Choice

A population of 800 beetles is growing each month at a rate of 5%. Find how many beetles there will be after 8 months. DO WE HAVE X or Y?!

• We have y! 

• We have x!

• We have x and y!

• We don't have either! 

Multiple Choice

If a 200 milligram dosage of Advil is taken and it decreases at a rate of 12% per house, how many of the milligrams will remain in the body 12 hours later? DO WE HAVE x or y?

• We have y! 

• We have x!

• We have x and y!

• We don't have either! 

Multiple Choice

You deposit $200 into a bank account that earns 5% interest yearly. When will the account have a balance of $600? Do we have x or y? 

• We have y! 

• We have x!

• We have x and y!

• We don't have either! 

Now, we are going to solve them!

​1) Set up the equation

​2) Identify which variable you HAVE and replace it in the equation!

​x=TIME

​y=TOTAL

​

​3) If you have ___, just plug it into the equation to find your answer!

​If you have ____, enter your equation in desmos and y=# and see where they cross!

Multiple Choice

Wanda bought a car for $32,450 from Honda. It depreciates as soon as you drive it off the lot by 16%. What is the equation for this?

• $$y=32450\left(1.16\right)^x$$  

• $$y=32450\left(.84\right)^x$$  

• $$y=16\left(32.45\right)^x$$  

• $$y=32450\left(1.016\right)^x$$  

Multiple Choice

Wanda bought a car for $32,450 from Honda. It depreciates as soon as you drive it off the lot per year by 16%. How much will the car be worth after 2 years?

• $22,896.72

• $43,664.72

• $830.72

Multiple Choice

Brayden started a skateboarding business with $560. His profit grew by 5.6% per year. Which equation represents this situation?

• $$y=560\left(1.56\right)^x$$  

• $$y=5.60\left(1.056\right)^x$$  

• $$y=560\left(1.056\right)^x$$  

• $$y=560\left(.944\right)^x$$  

Multiple Choice

Brayden started a skateboarding business with $560. His profit grew by 5.6% per year. How much will he make after 9 years?

• $333.37

• $306414.57

• $9144.57

• $914.45