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

Tags

CCSS.HSF-LE.A.1C

Which equation matches the graph?

Tags

CCSS.HSF.LE.A.2

Match each exponential expression to its equivalent logarithmic form.

• 4^x = 10

• log x = 4

• x¹⁰ = 4

• ln x ≈ 10

• 10⁴ = x

• ln 10 ≈ x

• e¹⁰ ≈ x

• log_x 4 = 10

• e^x ≈ 10

• log₄ 10 = x

Tags

CCSS.HSF.BF.B.5

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

Tags

CCSS.HSF.LE.A.4

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

Tags

CCSS.HSF-LE.A.1C

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

Tags

CCSS.HSF-IF.C.8B

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)

Tags

CCSS.HSF-BF.B.4A