# Exponential Growth and Decay

• Jun 4th 2010, 01:01 PM
Hockey_Guy14
Exponential Growth and Decay
a) If a boat slows according to an exponential function, and its initial speed was 40km/h, what does the formula need to be if the boat is only going 10km/h and it has been 10 minutes since letting off the gas? Define the variables

b) How fast was the boat going 1 minute after letting off the gas?

c) How fast will it be going 15 minutes after letting off the gas?

d) How long does it take to cut the boats original 40km/h speed in half?

Im having trouble figuring out the formula needed to determine the answers. Any help would be great. Thanks
• Jun 4th 2010, 01:23 PM
e^(i*pi)
Quote:

Originally Posted by Hockey_Guy14
a) If a boat slows according to an exponential function, and its initial speed was 40km/h, what does the formula need to be if the boat is only going 10km/h and it has been 10 minutes since letting off the gas? Define the variables

b) How fast was the boat going 1 minute after letting off the gas?

c) How fast will it be going 15 minutes after letting off the gas?

d) How long does it take to cut the boats original 40km/h speed in half?

Im having trouble figuring out the formula needed to determine the answers. Any help would be great. Thanks

The standard exponential decay formula is $\displaystyle A(t) = A_0e^{-kt}$ where

• A(t) = Amount left at any given time
• A_0 = Amount at time 0
• e = the base of the natural logarithm
• k = a positive constant
• t = time

In part a you are given A(t), A_0 and t so use those to find k
• Jun 4th 2010, 01:52 PM
Hockey_Guy14
We dont use that formula, we use Y=A(1+r)^n when trying to solve these, so any help on how to arrange it using this formula?
• Jun 6th 2010, 04:40 AM
skeeter
Quote:

Originally Posted by Hockey_Guy14
We dont use that formula, we use Y=A(1+r)^n when trying to solve these ... in future, please make sure that such information is provided in your original post.

$\displaystyle v = 40(1+r)^t$ , where $\displaystyle v$ is in km/hr and $\displaystyle t$ is in hrs

at $\displaystyle t = \frac{1}{6}$ hr (10 minutes) , $\displaystyle v= 10$

$\displaystyle 10 = 40(1+r)^{\frac{1}{6}}$

solve for $\displaystyle r$ to get the boat's speed as a function of time.
• Jun 6th 2010, 04:42 AM
Hockey_Guy14
Ahh I get it now..thanks alot eh..appreciate it :)