The value of the property in a particular block follows a pattern of exponential growth. In the year 2001, your company purchased a piece of property in this block. The value of the property in thousands of dollars, t years after 2001 is given by the exponential growth model

Since we are looking for the value of the property,
what variable are we seeking? If you said *V* you are right
on!!!!

Note that even though we are using*V* instead of *A*, the
concept of and formula for exponential growth is the same as discussed
in the lesson.

The way the problem is worded, 2001 is what we call our initial year. This is where*t* = 0.

Plugging in 0 for t and solving for*V* we get:

Note that even though we are using

The way the problem is worded, 2001 is what we call our initial year. This is where

Plugging in 0 for t and solving for

*

While writing up the final answer, keep in mind that
the problem said the value was in thousands of dollars.

**In 2001, the value of the property was $500,000.**

We could have also approached this problem by noting that the year was 2001, which is our initial year, so basically it was asking us for the initial worth, which is*V*o (*A*o in the formula).
This happens to be the number in front of *e* which is 500 in
this problem.

The reason I showed you using the formula was to get you use to it. Just note that when it is the initial year,*t* is 0,
so you will have *e* raised to the 0 power which means it will
simplify to be 1 and you are left with whatever *V*o (*A*o)
is.

We could have also approached this problem by noting that the year was 2001, which is our initial year, so basically it was asking us for the initial worth, which is

The reason I showed you using the formula was to get you use to it. Just note that when it is the initial year,

In the general growth formula, *k* is a constant
that represents the growth rate. *k* is the coefficient of *t* in *e*’s exponent.

So what would be our answer in terms of percent?

Well,*k* = .055, so **converting that to percent we get 5.5%** for our answer.

So what would be our answer in terms of percent?

Well,

Since we are looking for the population, what variable
are we looking for? If you said *V* give yourself a high
five.

What are we going to plug in for*t* in this problem?

Our initial year is 2001, and since*t* represents years after
2010, we can get *t* from 2010 - 2001, which would be 9.

Plugging in 9 for*t* and solving for *V* we get:

What are we going to plug in for

Our initial year is 2001, and since

Plugging in 9 for

Keep in mind that the problem said that the value was
in thousands of dollars.

**The value of the property in 2010 would be approximately
$820,249.12.**

Again, it looks like we have a little twist here.
Now we are given the value of the property and we need to first find *t* to find out how many years after 2001 we are talking about and then
convert that knowledge into the actual year.

We will still be using the same formula we did to answer the questions above, we will just be using it to find a different variable.

Plugging in 750 for*V* and solving for *t* we get:

We will still be using the same formula we did to answer the questions above, we will just be using it to find a different variable.

Plugging in 750 for

This means a little over 7 years after 2001, the value
of the property will be 750 thousand dollars.

**So our answer is during the year 2008.**

An artifact originally had 10 grams of carbon-14
present. The decay model describes the
amount of carbon-14 present after t years.

What are we going to plug in for *t* in this
problem?

Since*t* represents the number of years, it looks like we will
be plugging in 25,000 for *t*.

Plugging in 25000 for*t* and solving for *A* we get:

Since

Plugging in 25000 for

*replace

If we are looking for the half-life of carbon-14, what
variable are we looking for? If you said *t* give yourself
a high five!!!!

It looks like we don’t have any values to plug into*A*.
However, the problem did say that we were interested in the HALF-life,
which would mean ½ of the original amount (10) would be
present at the end (*A*). This means *A* can be
replaced with 10/2 = 5.

Replacing*A* with 5 and solving for *t* we get:

It looks like we don’t have any values to plug into

Replacing

Last revised on March 23, 2011 by Kim Seward.

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