Video Transcript
Rachel bought her house for 120000
dollars. Her house increased in value by two
percent per year and the value of her house after 𝑛 years can be calculated using
the equation 𝑉 equals 120000 times 𝑥 to the 𝑛 power. What is the value of 𝑥 in the
equation?
The value of Rachel’s house after
𝑛 years is 120000 times 𝑥 to the 𝑛 power. There are a few ways we could think
about this. We know that her house increases by
two percent per year. If we wanted to calculate the
increased value of her home after year one, we would start with the original value,
and we would add the increase. To calculate how much the value
increased, we would multiply 120000 by 0.02. When we write two percent as a
decimal, it becomes 0.02. And what’s happening here is we are
calculating this in year one. So, we only multiply it by 0.02 to
the first power.
But this equation that we’ve drawn
out, the original value plus the increase, doesn’t match exactly the equation we
we’re given. Because there is 120000 in both of
these terms, we can take that out. When we do that, we’ll have 120000
times one plus 0.02. This is because we need to find the
whole value of the house. And that’s represented by the whole
number one, plus the increase, which is represented by the two percent, or in this
case 0.02. And that means we need to plug in
1.02 in for the value of 𝑥, which gives the whole plus the two percent
increase. And we have the 𝑛 variable that
accounts for the number of years that have passed.
