Question

Help! Using an exponential model for this data, estimate when the building value will drop below 3,000.

Answer 1

Step 1

Graph the function and generate the exponential model.

The modeled function will be;

`y=12112.7(0.930332)^x`

Step 2

Find when the value will drop below $3000

`\begin{gathered} 3000=12112.7(0.930332)^x \\ 12112.7\cdot \:0.930332^x=3000 \\ 12112.7\cdot \:0.930332^x\cdot \:10=3000\cdot \:10 \\ 121127\cdot \:0.930332^x=30000 \\ (121127\cdot \:0.930332^x)/(121127)=(30000)/(121127) \\ 0.930332^x=(30000)/(121127) \\ x\ln \left(0.930332\right)=\ln \left((30000)/(121127)\right) \\ x=(\ln \left((30000)/(121127)\right))/(\ln \left(0.930332\right)) \\ x=19.32653 \end{gathered}`

Hence the answer will be;

`\begin{gathered} Year\text{ 19 tallies with 2009 and by this year the buiding value= \$3000} \\ Above\text{ this year the building value drops below \$3000} \\ Hence\text{ the answer is the value willl drop below \$3000 in 2010} \end{gathered}`