Test Questions on Solving Exponential Growth Applications (High School Algebra).

📚 Quick Study Guide

• 📈 Exponential Growth: Occurs when a quantity increases by the same percentage over a given period.
• 📝 General Formula: $y = a(1 + r)^t$, where:
  • $y$ = final amount
  • $a$ = initial amount
  • $r$ = growth rate (as a decimal)
  • $t$ = time
• 💡 Growth Rate: If the rate is given as a percentage, divide by 100 to convert it to a decimal (e.g., 5% = 0.05).
• 📅 Time Unit: Make sure the time unit for the rate and the time variable are the same (e.g., if the rate is per year, time should be in years).
• 🧮 Solving Problems: Identify the initial amount, growth rate, and time, then plug them into the formula and solve for the unknown.

🧪 Practice Quiz

1. A population of bacteria doubles every hour. If the initial population is 500, what will the population be after 4 hours?
   1. 1,000
   2. 4,000
   3. 8,000
   4. 16,000
2. The number of students at a school is increasing by 8% per year. If there are currently 1200 students, how many students will there be in 5 years?
   1. 1680
   2. 1763
   3. 1700
   4. 1740
3. An investment of $5,000 grows at an annual rate of 6%. Approximately, how much will the investment be worth after 10 years?
   1. $8,954
   2. $8,000
   3. $9,500
   4. $8,500
4. A rare species of frog is increasing in population at a rate of 12% per year. If there are currently 200 frogs, how many frogs will there be in 3 years?
   1. 281
   2. 300
   3. 250
   4. 320
5. The value of a house increases by 3% each year. If the house is currently worth $250,000, what will its value be in 7 years?
   1. $300,000
   2. $307,371
   3. $290,000
   4. $310,000
6. A mold culture doubles in size every day. If it starts with an area of 2 $mm^2$, what area will it cover after 6 days?
   1. 64 $mm^2$
   2. 128 $mm^2$
   3. 32 $mm^2$
   4. 256 $mm^2$
7. The number of views on a video is increasing by 15% each day. If the video initially had 500 views, how many views will it have after 5 days?
   1. 900
   2. 1006
   3. 1100
   4. 1050