Unit 4 Lesson 2

In 1990, the value of a home is $170,000. Since then, its value has increased by 5% per year. What is the approximate value of the home in the year 1993?

• about $196,600

• about $196,800

• about $197,000

• about $197,200

In 1990, the value of a home is $170,000. Since then, its value has increased by 5% per year. What equation, in function notation, represents the value of the home as a function of time in years since 1990, $t?$  

•  $v\left(t\right)=170,000\cdot\left(t\right)^{\left(0.05\right)}$  

•  $v\left(t\right)=170,000\cdot\left(t\right)^{1.05}$  

•  $v\left(t\right)=170,000\cdot\left(0.05\right)^t$  

•  $v\left(t\right)=170,000\cdot\left(1.05\right)^t$  

In 1990, the value of a home is $170,000. Since then, its value has increased by 5% per year. Will the value of the home be more than $500,000 in 2020 (assuming that the trend continues)? Explain your reasoning.

The graph shows a wolf population which has been growing exponentially. What was the population when it was first measured?

The graph shows a wolf population which has been growing exponentially. By what factor did the population grow in the first year?

The graph shows a wolf population which has been growing exponentially. Which equation shows the relationship of the wolf population,  $w,$  and the number of years since it was measured,  $t.$  

•  $w=100\cdot\left(\frac{6}{5}\right)^t$  

•  $w=\left(\frac{6}{5}\right)^t$  

•  $w=100\cdot\left(t\right)^{\frac{6}{5}}$  

•  $w=\left(t\right)^{\frac{6}{5}}$  

Here is the graph of an exponential function $f.$  Find an equation defining  $f.$  Explain your reasoning.