Exponential Growth & Logarithmic Conversions Quiz

A population of bacteria doubles every 3 hours. If there are initially 500 bacteria, how many will there be after 12 hours? Graph the exponential growth function.

• 10000

• 4000

• 8000

• 2000

The half-life of a certain radioactive substance is 5 years. If you start with 80 grams, how much will remain after 15 years? Use logarithms to find the time when only 10 grams remain.

• 5 grams, 10 years

• 10 grams, 15 years

• 20 grams, 25 years

• 40 grams, 30 years

A car's value decreases exponentially over time. If a car is worth $20,000 today and loses 15% of its value each year, what will its value be in 5 years? Graph the depreciation function.

• $5,000

• $10,000

• $15,000

• The value of the car in 5 years will be approximately $8,874.20.

The formula for compound interest is A = P(1 + r/n)^(nt). If you invest $1,000 at an annual interest rate of 5% compounded quarterly, how much will you have after 10 years? Convert the formula to logarithmic form to find the time needed to double your investment.

• $1,200 after 10 years

• $2,000 after 10 years

• It will take about 10 years to double your investment

• After 10 years, you will have approximately $1643.62. It will take about 17.67 years to double your investment.

A certain species of fish grows exponentially. If the population is currently 200 and grows at a rate of 25% per year, how many fish will there be in 4 years? Graph the growth function and identify the y-intercept.

• 700

• 600

• 400

• 543

If log_b(64) = 2, what is the value of b? Convert this logarithmic equation to its exponential form and solve for b.

• 8

• 10

• 4

• 16

A bank offers an account with an interest rate of 4% compounded annually. If you want to have $5,000 in the account after 10 years, how much do you need to deposit now? Use logarithms to solve for the initial deposit amount.

• 3377.96

• 4000.00

• 2500.00

• 5000.00

The number of users of a new app is modeled by the function N(t) = 1000e^(0.3t), where t is the time in months. How many users will there be after 6 months? Graph the function and identify the growth rate.

• Approximately 3000 users after 6 months.

• Approximately 1500 users after 6 months.

• Approximately 6050 users after 6 months.

• Approximately 8000 users after 6 months.

A scientist measures the decay of a substance and finds that after 8 hours, 25% of the original amount remains. If the original amount was 200 grams, how much is left after 16 hours? Use logarithms to determine the decay constant.

• 100 grams

• 12.5 grams

• 50 grams

• 6.25 grams

The equation y = 3^x represents the growth of a plant species. If the plant reaches a height of 81 cm, what is the value of x? Convert the equation to logarithmic form to find the solution.

• 2

• 5

• 10

• 4