Advanced Math - Chapter 3 Review

Front

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

Back

The y-intercept (initial value) is 13.

Front

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

Back

The equation is y=5000(0.7)^x.

Front

Evaluate \( \log_{ }\left(\sqrt[5]{100}\right) \)

Back

The answer is \( \frac{2}{5} \).

Front

Write an equation that models Samantha's hair growth, starting at 6 inches and growing at a rate of 14% a week.

Back

The equation is y=6(1.14)^x.

Front

Solve for x: \( \log_6x=3 \)

Back

The solution is x=216.

Front

What does the base of a logarithm represent in a logarithmic function?

Back

The base indicates the number that is raised to a power to obtain a given number.

Front

Define exponential decay.

Back

Exponential decay occurs when a quantity decreases at a rate proportional to its current value.

Front

What is the general form of an exponential growth function?

Back

The general form is y = a(1 + r)^t, where a is the initial amount, r is the growth rate, and t is time.

Front

How do you convert a logarithmic equation to its exponential form?

Back

If \( \log_b(a) = c \), then it can be rewritten as \( b^c = a \).

Front

What is the initial value in the function f(x)=a(1+r)^x?

Back

The initial value is 'a', which represents the starting amount before growth.