Question

At the moment a hot iron rod is plunged into freezing water, the difference between the rod's and the water's temperatures is 100\degree100°100, degree Celsius. This causes the iron to cool and the temperature difference drops by 60\%60%60, percent every second. Write a function that gives the temperature difference in degrees Celsius, D(t)D(t)D, left parenthesis, t, right parenthesis, ttt seconds after the rod was plunged into the water.

Answer 1

Answer:

$D(t)=100(0.4)^t$

Step-by-step explanation:

The temp is 100 at time t = 0

After 1 sec, the temp difference would be:

$100-(\frac{100-60}{100})$

After 2 sec, the temp difference would be:

$100-(\frac{100-60}{100})^2$

Similarly for 3 seconds, 4 seconds etc.

We notice that the parenthesis part is 40% of it, so we can also write:

100(40%)^t,

where

t is the time

40% can be written as 40/100  = 0.4

SO, the function is:

$d(t)=100(0.4)^t$

Answer 2

Answer:

$D(t)=100*0.4^t$

Step-by-step explanation:

Initially, the difference between the rod's and the water's temperatures is 100°

i.e D(t)=100 When t=0

After 1 seconds, the temp drops by 60%.

Therefore, the new value of D will be the old value multiplied by (100-60)%.

D(1)=100 X (100%-60%) = 100*0.4

After 2 seconds, the temp difference would be:

D(2)=100*0.4*0.4= $100*0.4^2$

We notice that for any t, the percentage at which the difference is reduced is raised to the power of t.

Therefore, temperature difference in degrees Celsius, D(t), t seconds after the rod was plunged into the water is given as:

$D(t)=100*0.4^t$