12/03 - CTG: Exponential Functions Review

Front

What is the domain of the function y=2^x?

Back

The domain is all real numbers.

Front

What is the range of the function y=2^x?

Back

The range is y > 0.

Front

What type of function is characterized by a rapid increase in value as x increases?

Back

Exponential Growth.

Front

What type of function is characterized by a rapid decrease in value as x increases?

Back

Exponential Decay.

Front

How do you model exponential decay mathematically?

Back

Use the formula f(t) = a(1 - r)^t, where a is the initial amount and r is the decay rate.

Front

What is the y-intercept of the function f(x)=13(0.27)^x?

Back

The y-intercept (initial value) is 13.

Front

How do you write an exponential function for depreciation?

Back

Use the formula V(t) = P(1 - r)^t, where P is the initial value and r is the depreciation rate.

Front

What is the formula for exponential growth?

Back

f(t) = P(1 + r)^t, where P is the initial amount and r is the growth rate.

Front

If a quantity decreases by 5% each hour, what is the multiplier for the function?

Back

The multiplier is 0.95.

Front

What is the initial value in the function f(h) = 75(0.95)^h?

Back

The initial value is 75 gallons.