The weight of a termite mound (y) in kilograms is measured each month (x) after it was first found. The mound after 1 month is found to be 2 kilograms and after 3 months it is measured at 18 kilograms. It is believed that the model connecting the weight of the mound to the number of months is either an exponential model of a power model. Discuss which of the two models you think would be more appropriate for the above scenario. You may want to consider initial conditions and rates of the change above

Question

The weight of a termite mound (y) in kilograms is measured each month (x) after it was first found. The mound after 1 month is found to be 2 kilograms and after 3 months it is measured at 18 kilograms. It is believed that the model connecting the weight of the mound to the number of months is either an exponential model of a power model. Discuss which of the two models you think would be more appropriate for the above scenario. You may want to consider initial conditions and rates of the change above

There were previous sections which I had to graph an exponential and power curve with the same coordinates of (1,2) and (3,18).

Now I am unsure if its a power of exponential. I would think it would be exponential as you can't find a mound at 0 kgs otherwise it would not be found if there is nothing to be found. I'm not 100% certain, so can anyone verify?

Answer 1

To determine whether an exponential or power model would be more appropriate for the given scenario, we need to consider the initial conditions and rates of change.

In an exponential model, the value of the dependent variable (in this case, the weight of the termite mound) increases or decreases proportionally to the exponential function of the independent variable (in this case, the number of months). The general form of an exponential function is y = a*b^x, where a and b are constants.

In a power model, the value of the dependent variable changes proportionally to a power function of the independent variable. The general form of a power function is y = a*x^b, where a and b are constants.

Now let's analyze the given data points: after 1 month, the weight of the mound is 2 kilograms, and after 3 months, it is 18 kilograms.

If we consider an exponential model, we can put the values into the general equation: 2 = a*b^1 and 18 = a*b^3. Dividing the second equation by the first equation eliminates the constant 'a,' leaving us with 9 = b^2. Solving for 'b' gives us two possible solutions: b = 3 or b = -3.

However, if b = -3, it does not make sense in this context as it would result in negative weights. Therefore, we can reject the option of using an exponential model.

Alternatively, if we consider a power model, we can put the values into the general equation: 2 = a*1^b and 18 = a*3^b. Dividing the second equation by the first equation eliminates the constant 'a,' leaving us with 9 = 3^b. Solving for 'b' gives us b = 2.

Thus, the power model, y = a*x^2, would be more appropriate for this scenario as it accurately represents the relationship between the weight of the termite mound and the number of months.

Please note that this is just one approach to determining the appropriate model based on the given data points. It is always a good practice to check for other factors and evaluate different models to ensure the most accurate representation.