Question

Josephina is preparing Indian pudding for a party. She is cooking the pudding in a water-tight container submerged in boiling water. When the pudding is done, Josephina places the container of pudding out in the snow to cool down. When Josephina places the Indian pudding in the snow, the temperature of the pudding is 100°C. After 1 minute, the temperature of the pudding drops to 95°C.

a. Assuming the temperature is dependent on the minutes the pudding remains in the snow, formulate an exponential function to represent the problem situation.
Explain your process.

b. Graph the exponential function over an appropriate domain and range. Identify the key attributes including domain, range, intercept(s), and asymptotic behavior
and describe their meaning in the problem situation.
c. Josephina wants to serve the pudding when it is at a temperature of 10°C. How long will she need to leave the Indian pudding cooling in the snow for it to reach the desired temperature? Solve the problem algebraically, and round the answer to the nearest minute.

Answer 1

a) T(t)= 100e^(-0.0513t)

b) See attachment for graph

y-intercept is inital temperature

domain is t≥0, range is 0 <T≤100

c) 44.9min

Explanation:

a) at t=0, T=100

at t=1, T=95

T(t)= Ae^-kt

100=Ae^(-k×0)

A=100

95=100e^(-k

k=0.0513

T(t)= 100e^(-0.0513t)

b) as time reaches infinity, temperature of pudding becomes approximately equal to 0. x-axis is the asyptote of the graph

c) 10= 100e^(-0.0513t)

t= 44.9 min