Question

The function y = 55−2.8x models the amount of water in a bathtub while it is draining for x minutes. Which of the following statements properly interprets a key feature of the model?(1 point) Responses The bath is draining at a rate of 55 gallons per minute The bath is draining at a rate of 55 gallons per minute The amount of water in the bath increases by 2.8 gallons each minute The amount of water in the bath increases by 2.8 gallons each minute Before any water drained, the bath contained 2.8 gallons of water Before any water drained, the bath contained 2.8 gallons of water Before any water drained, the bath contained 55 gallons of water Before any water drained, the bath contained 55 gallons of water Question 2 Kamran invests $1800 into an account. The amount of money in his account grows at a rate of 3.1% each year. Kamran builds a model to represent the amount of money in his account over the next 10 years. Which of the following are key features of the graph?(1 point) Responses The graph has a y-intercept of (0, 1800) The graph has a y-intercept of (0, 1800) The graph is a straight line The graph is a straight line The graph shows a decreasing function The graph shows a decreasing function The graph has a relative maximum

Answer 1

Question 1:

The function \( y = 55 - 2.8x \) models the amount of water in a bathtub as it drains over time \( x \) in minutes. In this equation, the water level decreases over time because the coefficient of \( x \) is negative (-2.8), indicating that the water is draining.

The correct interpretation from the provided options is:

• Before any water drained, the bath contained 55 gallons of water.

When \( x = 0 \), substituting into the equation gives \( y = 55 - 2.8(0) = 55 \). So, initially, the bathtub had 55 gallons of water.

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Question 2:

Kamran's investment of $1800 with a growth rate of 3.1% each year can be modeled using an exponential growth function. The key features of the graph would include information about the initial investment and the nature of the growth.

The correct interpretation from the provided options is:

• The graph has a y-intercept of (0, 1800).

This is because the y-intercept represents the initial amount of money in the account, which is $1800 at year 0.

The other responses are incorrect because:

• The graph is not a straight line; it would be a curve due to exponential growth.
• The graph shows an increasing function as the money grows over time.
• It does not have a relative maximum but demonstrates continuous growth.

Therefore, for each question:

1. Before any water drained, the bath contained 55 gallons of water.
2. The graph has a y-intercept of (0, 1800).