Question

The amount of caffeine present in the human body after consumption can be modelled by an exponential function of the form C= AxB^t where t is the elapsed time, in hours, and C is the amount of caffeine remaining, in milligrams. In the morning, Steve drinks a Monster Energy ™ and in the evening he prefers Code Red Mountain Dew© before he plays Pokémon®. The equations of the exponentials functions that model Steve’s caffeine consumption are shown below.

Monster Energy C= 55 (1/2)^t Mountain Dew C=110 (1/2)^T

Using the numerical values in the functions above, compare the information that these values provide

Answer 1

Monster Energy $C= 55 (1/2)^t$

Initial amount $C_0=A= 55 mg.$

The half-life of caffeine is $\tau=1$ hour.

The amount of caffeine is decreased by $1/B=2$ times (halved) every hour.

Mountain Dew $C= 110 (1/2)^t$

Initial amount $C_0=A= 110 mg.$

The half-life of caffeine is $\tau=1$ hour.

The amount of caffeine is decreased by $1/B=2$ times (halved) every hour.