Question

I wanted to take a bath so I filled my tub up with water. Every 15 minutes the temperature in my bathtub got 10% colder. The original temperature of my bath water was 40 degrees celsius.

a) Graph the function ​

Answer 1

A graph of the exponential function that models the temperature is shown on the coordinate plane in the image below.

In Mathematics and Statistics, a population or temperature that decreases at a specific period of time represents an exponential decay.

This ultimately implies that, a mathematical model for any population or material that decreases by r percent per unit of time is an exponential function of this form:

`P(t) = I(1 - r)^t`

Where:

• P(t) represents the final population or temperature.
• t represents the time or number of years or days.
• I represents the initial population or temperature.
• r represents the decay rate.

Since every 15 minutes the temperature in my bathtub got 10% colder, an exponential function that models the situation is given by;

`P(t) = I(1 - r)^t\\\\P(t) = 40(1 - 0.10)^(t)/(15)\\\\P(t) = 40(0.90)^(t)/(15)`