21.07 Growth and decay (Extended)
Interactive practice questions
Consider the graph shown.
Which of the following relationships could be represented by the given graph?
The number of handshakes, $y$y, made by $x$x people in a room if every person shakes hands with every other person.
The number of layers, $y$y, resulting from a rectangular piece of paper being folded in half $x$x times.
The number of people, $y$y, attending a parent/teacher conference when there are $x$x parents who each bring $2$2 children.
What does the $y$y-intercept of the curve represent?
The number of folds that it would take to reach $8$8 layers of paper.
That there are $2$2 layers of paper after $1$1 fold has been made.
That the paper is rectangular before any folds are made.
That there is $1$1 layer of paper when no folds have been made.
The equation of the graph is $y=2^x$y=2x.
If a rectangular piece of paper is folded $10$10 times, determine the resulting number of layers.
When a coin is flipped, there are two possible outcomes: heads (H) or tails (T).
A sample contains $1$1 gram of Ruthenium-106, which has a half-life of one year.
An initial chemical reaction results in a chain of chemical reactions that follow.
The total number of reactions after $t$t seconds is given by the equation $y=4^t$y=4t.