IB Modelling Quiz

Using the image given, find a formula for converting a temperature in degrees Fahrenheit to degrees Celsius.

Answer explanation

To convert Fahrenheit to Celsius, use the formula C = (F - 32) × 5/9. This formula subtracts 32 from the Fahrenheit temperature and then multiplies the result by 5/9 to get the Celsius equivalent.

Find the temperature in degrees Celsius that is recorded as 77 degrees Fahrenheit.

Answer explanation

To convert 77°F to Celsius, use the formula C = (F - 32) × 5/9. Plugging in the values: C = (77 - 32) × 5/9 = 25°C. Therefore, 77 degrees Fahrenheit is equivalent to 25 degrees Celsius.

Over one year, the mean daily temperature in Mexico City was calculated to be 17 degrees Celsius. For the same year, find in degrees Fahrenheit.

Answer explanation

To convert Celsius to Fahrenheit, use the formula F = (C × 9/5) + 32. For 17°C, F = (17 × 9/5) + 32 = 62.6°F. Thus, the mean daily temperature in Mexico City is 62.6 degrees Fahrenheit.

Use the model to find an expression for m in terms of h.

Answer explanation

  𝑚 = 𝑎ℎ^3

125ℎ^3

Hence find the mass of a different cheetah, with a shoulder height of 0.75 metres.

Answer explanation

= 52.7kg

Find the value of k.

Answer explanation

= 2.28

Find the percentage of power in the phone at 07:00.

Answer explanation

= 40%

The percentage of power in the phone reaches 75 % at 08:00.

Find the value of a.

Answer explanation

= 2.4

Draw the graph of P=100-60×a^-t on the following set of axes.

do this in your book or on paper and your teacher will come around to check.

State a mathematical reason why the model predicts the percentage of power in the phone will never reach 100%.

Answer explanation

The model uses a mathematical function that approaches but never reaches 100%, shown by an asymptotic function. This means the percentage of power will get closer to 100% but will always remain just below it.