Solving Exponential Growth and Decay with Logarithms

• Linear Growth

• Linear Decay

• Exponential Growth

• Exponential Decay

Solving exponential equations using logarithms: Solve the equation 2^x = 16 using logarithms

• x = 4

• x = 8

• x = 10

• x = 2

Solving exponential equations using logarithms: Find the value of x in the equation 4^x = 64 using logarithms

• 16

• 3

• 8

• 2

Understanding the relationship between exponential and logarithmic functions: Explain the relationship between the exponential function f(x) = 3^x and its corresponding logarithmic function

• They are inverse functions of each other.

• They have no relationship

• The exponential function is a subset of the logarithmic function

• They are parallel functions

Write b^k = m into logarithmic form.

• log _b m = k

• log _m k = b

• log _b k = m

• log _k m = b

The number of mosquitoes at the beginning of the summer was 4,000. The population of mosquitoes is expected to grow at a rate of 25% a month. How many mosquitoes will there be after 4 months?

• 9766

• 9006

• 9765

• 5433

A population of fish starts at 8,000 and decreases by 6% per year. What is the population of fish after 10 years?

• 14327

• 4309

• 839

• 7680

Write an equation that models the following situation:
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.

• y=6(0.14)^x

• y=6(1+14)^x

• y=6(1.14)^x

• y=6(0.86)^x

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

• y=5000(0.7)^x

• y=30(5000)^x

• y=5000(1.3)^x

• y=5000x^x

If you have $10, and your money doubles every year, how much money will you have in 10 years?

• $50

• $100

• $5120

• $10240