Exponential Functions and Population Dynamics

The video tutorial explains how to find the equation of an exponential function in a word problem context. It begins with a refresher on exponential functions, highlighting the roles of the initial value and growth or decay factors. Two examples are provided: one involving fish population growth and another modeling antibiotic decay. The tutorial demonstrates how to set up and solve exponential equations using given data points.

What is the general form of an exponential function?

• f(x) = a/b^x

• f(x) = a + bx

• f(x) = a * b^x

• f(x) = ax^b

In an exponential function, what does 'a' represent?

• The decay factor

• The growth factor

• The exponent

• The initial value

What must be true about the growth or decay factor 'b' in an exponential function?

• b must be equal to one

• b must be negative

• b must be zero

• b must be greater than zero and not equal to one

In the fish population problem, what is the independent variable?

• The number of fish

• The time in days

• The initial number of fish

• The growth factor

How many fish were there after one day in the fish population problem?

• 107

• 100

• 114

• 120

What equation represents the fish population after one day?

• p(t) = a * b^2

• p(t) = a * b^t

• p(t) = a * b^1

• p(t) = a * b^0

What is the approximate value of the growth factor 'b' in the fish population problem?

• 1.08

• 1.05

• 1.06

• 1.07

In the antibiotic dosage problem, what is the initial amount of antibiotic taken?

• 500 mg

• 400 mg

• 600 mg

• 300 mg

After one hour, how much of the antibiotic remains in the body?

• 200 mg

• 400 mg

• 100 mg

• 300 mg

What is the decay factor 'b' in the antibiotic dosage problem?

• 1/4

• 1/3

• 1

• 1/2