Solving Exponential Growth and Decay with Logarithms

A population of fish starts at 6,500 and decreases by 8% per year. What is the population of fish after 10 years?

*Answer with the number value only

**Round appropriately

Which equation matches the graph?

Match each exponential expression to its equivalent logarithmic form.

• 4^x = 10

• log x = 4

• x¹⁰ = 4

• log_x 4 = 10

• e^x ≈ 10

• ln 10 ≈ x

• e¹⁰ ≈ x

• ln x ≈ 10

• 10⁴ = x

• log₄ 10 = x

Mathematical Equivalence

ON

A radioactive substance decays at a rate of 5% per year. If the initial amount of the substance was 100 grams, how much will remain after 20 years?

• 35.85 grams

• 37.69 grams

• 40.10 grams

• 42.58 grams

A colony of termites is growing continuously at a rate of 6.2% monthly. If the colony starts with 500, how many would there be in one year?

(Enter only the value in the blank. Round to the nearest whole number.)

Mathematical Equivalence

ON

Hint: use a graph and/or table of values to determine the answer

• approximately 16 years

• approximately 6 years

• approximately 10 years

If the population of a city is increasing exponentially and triples every 10 years, what is the population after 30 years if the initial population was 2000?

• 6000

• 12000

• 18000

• 54000

Tags

DOK Level 1: Recall

What indicates growth or decay in f(x)= a⋅b^x

• If b is positive or negative

• If b is between 0 and 1 OR greater than 1

• If a is positive or negative

• If a is between 0 and 1 OR greater than 1

Find the inverse of the function f(x)=5^(x+2)

• f^-1(x)=log₅(x-2)

• f^-1(x)=log₅(x)-2

• f^-1(x)=log₅(x)+2

• f^-1(x)=log₅(x+2)