EOC Exponential Review

Front

What is the y-intercept (initial value) in the function f(x)=13(.27)^x?

Back

The y-intercept (initial value) is 13.

Front

Which function models the amount of money a child receives if it starts with a nickel and doubles every day?

Back

A(x) = 0.05(2)^x

Front

If a population of fish starts at 8,000 and decreases by 6% per year, what is the population after 10 years?

Back

The population after 10 years is approximately 4,309.

Front

What type of function is f(x)=2⋅(1/7)^x?

Back

Exponential Decay.

Front

If the mice population is 25,000 and decreases by 20% each year, what will be the population after 3 years?

Back

The population after 3 years is 12,800.

Front

Define exponential growth.

Back

Exponential growth occurs when a quantity increases by a consistent percentage over time.

Front

Define exponential decay.

Back

Exponential decay occurs when a quantity decreases by a consistent percentage over time.

Front

What is the formula for exponential growth?

Back

The formula is A(t) = A_0 * (1 + r)^t, where A_0 is the initial amount, r is the growth rate, and t is time.

Front

What is the formula for exponential decay?

Back

The formula is A(t) = A_0 * (1 - r)^t, where A_0 is the initial amount, r is the decay rate, and t is time.

Front

How do you find the initial value in an exponential function?

Back

The initial value is found by evaluating the function at x=0.