Spiral for FOM 1 with desmos

Front

What is an explicit function?

Back

An explicit function is a function where the dependent variable is expressed directly in terms of the independent variable, allowing for direct computation of output values.

Front

How do you identify the pattern in a sequence of numbers?

Back

To identify the pattern in a sequence, look for a consistent difference (arithmetic sequence) or a consistent ratio (geometric sequence) between consecutive terms.

Front

What is the explicit function for the arithmetic sequence 3, 7, 11, 15, ...?

Back

f(x) = 4x - 1.

Front

What is the explicit function for the geometric sequence 500, 250, 125, ...?

Back

f(x) = 1000(1/2)^x.

Front

What characterizes exponential decay?

Back

Exponential decay occurs when a quantity decreases at a rate proportional to its current value, often represented by a base less than 1 in the function.

Front

What is the formula for exponential decay?

Back

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

Front

How do you classify a model as exponential growth or decay?

Back

A model is classified as exponential growth if the base of the exponential function is greater than 1, and as decay if the base is between 0 and 1.

Front

What is the decay model for a culture of bacteria that dies by 30% each year starting with 5000 cells?

Back

y = 5000(0.7)^x.

Front

How do you evaluate a linear function at a specific point?

Back

To evaluate a linear function at a specific point, substitute the value of the independent variable into the function and simplify.

Front

What is the value of f(20) if f(x) = -9x + 12?

Back

f(20) = -168.