Function Notation: An ice cream cone is left in the hot sun. You notice that...

[Don't Drink and Derive]

1)So there's an ice cream cone left in the hot sun. You notice that every 5 min the ice cream cone loses 1/2 of it's volume. If starting volume was 125mL, what is the function of the volume(V) with respect to time(t).

First i wrote V(t)=125 then =125(1/2) for the volume it's losing and last step =125(1/2)^(t/5)

2)(i think i got this one right) I want to calculate the distance from my house to each of my friends'. if i drive at 50km/h. Need to create a function for distance(D) with respect to number of hours it takes to travel(t)

D(t)=50(t)

Thanks in advance!

 

[ksdhart2]

1)So there's an ice cream cone left in the hot sun. You notice that every 5 min the ice cream cone loses 1/2 of it's volume. If starting volume was 125mL, what is the function of the volume(V) with respect to time(t).

First i wrote V(t)=125 then =125(1/2) for the volume it's losing and last step =125(1/2)^(t/5)

I agree with your answer here. If you're ever unsure of an answer, you can always check it yourself. In this case, you'd check it by plugging some values of t and seeing if they make sense. For instance, if 5 minutes have passed, t=5 and thus V(t)=125*(1/2)^(5/5)=125*(1/2)=62.5. If t=15, V(t)=125*(1/2)^(15/5)=125*(1/2)^3=15.625. Do these values make sense? Do they fit with the shrinking volume laid out by the problem?

2)(i think i got this one right) I want to calculate the distance from my house to each of my friends'. if i drive at 50km/h. Need to create a function for distance(D) with respect to number of hours it takes to travel(t)

D(t)=50(t)!

If we're assuming, for simplicity's sake, that you always drive at a constant speed of 50 km/h, then I agree with your answer. A more "real world" answer would factor in changing speed, but that can get ugly in a hurry, so probably best to ignore it.

 

[Don't Drink and Derive]

Thanks!