Flashcard - Exponential Growth and Decay

Front

What does the model P=A(1+r)^t best represent?

Back

Exponential growth

Front

If a population of mosquitoes grows at a rate of 25% a month, how do you calculate the population after 4 months?

Back

Use the formula P = A(1 + r)^t, where A is the initial population, r is the growth rate, and t is the time in months.

Front

Classify the model A=1200(0.85)^6 as Exponential GROWTH or DECAY.

Back

Decay

Front

Which function shows an initial amount of $15 and an increase of 35% each year?

Back

y = 15(1.35)^x

Front

How do you determine the number of deer in a population that decreases by 1.5% per year?

Back

Use the function y = 1500(1 - 0.015)^t.

Front

Define Exponential Growth.

Back

Exponential growth occurs when the growth rate of a value is proportional to its current value, leading to growth that accelerates over time.

Front

Define Exponential Decay.

Back

Exponential decay occurs when a quantity decreases at a rate proportional to its current value, leading to a rapid decrease over time.

Front

What is the formula for Exponential Growth?

Back

P = A(1 + r)^t, where P is the future value, A is the initial amount, r is the growth rate, and t is time.

Front

What is the formula for Exponential Decay?

Back

P = A(1 - r)^t, where P is the future value, A is the initial amount, r is the decay rate, and t is time.

Front

If a population of 2000 decreases by 10% per year, what will the population be after 3 years?

Back

Use the formula P = 2000(1 - 0.10)^3 to find the population.