B. Your hot tub water is too cold. You increase the setting so that the temperature increases by 10% every 20 minutes.
D. You deposit $50 into your bank account every week.
Which of the following represent a geometric sequence? Check all that apply.
A. After hip surgery, your doctor tells you to walk 5 minutes a day. Each day thereafter, you should increase your walk time by 2 minutes.
B. Your hot tub water is too cold. You increase the setting so that the temperature increases by 10% every 20 minutes.
C. 400 mg of radioactive material is discovered. The amount of material decreases by 50% every day.
D. You deposit $50 into your bank account every week.
E. Your grandmother paid $103 for one share of Apple stock for your birthday present. Each year, the value of the stock grows by 8%.
5 answers
Every square meter of solar paneling produces 0.2 kilowatts of electricity. Which of the following models this situation?
linear function with a negative rate of change
linear function with a positive rate of change
exponential decay function
exponential growth function
linear function with a negative rate of change
linear function with a positive rate of change
exponential decay function
exponential growth function
Linear function with a positive rate of change
Mrs. Eaton's class is participating in the "Box Tops for Education" campaign. On the first day, her class collected 2 tops. On the third day, her class collected 8 tops. Let D represent each collection day and N represent the number of tops collected on that day.
Based on the situation, John claims the number of tops collected can be modeled by an exponential function. Riley disagrees and claims the number of tops can be modeled with a linear function. What is the number of tops collected on the sixth day based on the exponential model? What is the number of tops collected on the sixth day based on the linear model?
Number of tops on 6th day based on exponential model: blank
Number of tops on the 6th day based on the linear model: blank
Based on the situation, John claims the number of tops collected can be modeled by an exponential function. Riley disagrees and claims the number of tops can be modeled with a linear function. What is the number of tops collected on the sixth day based on the exponential model? What is the number of tops collected on the sixth day based on the linear model?
Number of tops on 6th day based on exponential model: blank
Number of tops on the 6th day based on the linear model: blank
To determine the number of tops collected on the sixth day based on the exponential and linear models, we need to first identify the pattern in the data.
Looking at the data given:
On the first day (D = 1), N = 2
On the third day (D = 3), N = 8
From the data, it seems that the number of tops collected is increasing by a factor of 4 (from 2 to 8) every two days.
Since the number of tops collected is increasing by a constant factor, it indicates an exponential growth model.
Based on this exponential growth model, we can find the number of tops collected on the sixth day (D = 6) by continuing the pattern.
Starting with N = 2 on the first day, and increasing by a factor of 4 every two days:
On the 6th day, N = 2 * 4 * 4 = 32
Therefore, based on the exponential model, the number of tops collected on the 6th day is 32.
Now, let's consider the linear model. A linear function has a constant rate of change. In this case, the rate of change from the first day to the third day is 6 tops per day (from 2 tops to 8 tops in two days).
Using this constant rate of change to predict the number of tops on the sixth day:
Rate of change = 6 tops per day
Starting point on the first day = 2 tops
Number of days from the first to the sixth day = 6 - 1 = 5 days
Using the formula for a linear model (y = mx + b), where m is the rate of change and b is the starting point:
N for the 6th day = 6 * 6 + 2 = 36 + 2 = 38
Therefore, based on the linear model, the number of tops collected on the 6th day is 38.
Looking at the data given:
On the first day (D = 1), N = 2
On the third day (D = 3), N = 8
From the data, it seems that the number of tops collected is increasing by a factor of 4 (from 2 to 8) every two days.
Since the number of tops collected is increasing by a constant factor, it indicates an exponential growth model.
Based on this exponential growth model, we can find the number of tops collected on the sixth day (D = 6) by continuing the pattern.
Starting with N = 2 on the first day, and increasing by a factor of 4 every two days:
On the 6th day, N = 2 * 4 * 4 = 32
Therefore, based on the exponential model, the number of tops collected on the 6th day is 32.
Now, let's consider the linear model. A linear function has a constant rate of change. In this case, the rate of change from the first day to the third day is 6 tops per day (from 2 tops to 8 tops in two days).
Using this constant rate of change to predict the number of tops on the sixth day:
Rate of change = 6 tops per day
Starting point on the first day = 2 tops
Number of days from the first to the sixth day = 6 - 1 = 5 days
Using the formula for a linear model (y = mx + b), where m is the rate of change and b is the starting point:
N for the 6th day = 6 * 6 + 2 = 36 + 2 = 38
Therefore, based on the linear model, the number of tops collected on the 6th day is 38.