Question

ap stats lesson 3.6 homework name chase coleman 1. for the relationships between each pair of variables below, determine which model would be most appropriate: linear, exponential, or power. a. explanatory: length of wall; response: gallons of paint needed to paint wall b. explanatory: year; response: amount of money in a savings account earning compound interest, with no withdrawals made c. explanatory: number of people at a party; response: number of pizzas ordered for the party

Explanation:

Step1: Analyze part a

The amount of paint needed is proportional to the area of the wall. Since area is a two - dimensional measure related to length by a power relationship (if we assume uniform height, area = length×height, which is a power relationship of degree 1 in terms of length for a fixed height), a power model is appropriate.

Step2: Analyze part b

The formula for compound - interest is $A = P(1 + r)^t$, where $A$ is the amount of money in the account, $P$ is the principal amount, $r$ is the interest rate per period, and $t$ is the number of periods. This is an exponential function of $t$, so an exponential model is appropriate.

Step3: Analyze part c

Typically, the number of pizzas ordered is directly proportional to the number of people at a party (assuming a relatively constant number of slices per person). If $y$ is the number of pizzas and $x$ is the number of people, $y=kx$ (where $k$ is a positive constant), which is a linear relationship.

Answer:

a. Power
b. Exponential
c. Linear