Writing Exponential Functions from Word Problems

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a(b)^x, where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent.

Front

What does the 'a' value represent in an exponential function?

Back

The 'a' value represents the initial value or y-intercept of the function, which is the value of the function when x = 0.

Front

How do you write an exponential function for growth?

Back

For growth, the function is written as f(x) = a(b)^x, where b > 1.

Front

How do you write an exponential function for decay?

Back

For decay, the function is written as f(x) = a(b)^x, where 0 < b < 1.

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is V(t) = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

Front

If a population triples every hour, how is this represented in an exponential function?

Back

This is represented as f(h) = a(3)^h, where 'a' is the initial population.

Front

What is the relationship between the base of an exponential function and growth/decay?

Back

If the base is greater than 1, the function represents growth; if the base is between 0 and 1, it represents decay.

Front

How do you determine the decay rate from an exponential function?

Back

The decay rate can be found by subtracting the base from 1 in the function V(t) = a(b)^t, where 0 < b < 1.

Front

Write an exponential function for a car that depreciates at 12% per year starting at $18,000.

Back

V(t) = 18000(0.88)^t.

Front

What does it mean if a function has a base of 0.7?

Back

A base of 0.7 indicates a decay rate of 30%, meaning the quantity decreases to 70% of its previous value each time period.