Step 1
Graph the function and generate the exponential model.
The modeled function will be;
[tex]y=12112.7(0.930332)^x[/tex]
Step 2
Find when the value will drop below $3000
[tex]\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 \\ \frac{121127\cdot \:0.930332^x}{121127}=\frac{30000}{121127} \\ 0.930332^x=\frac{30000}{121127} \\ x\ln \left(0.930332\right)=\ln \left(\frac{30000}{121127}\right) \\ x=\frac{\ln \left(\frac{30000}{121127}\right)}{\ln \left(0.930332\right)} \\ x=19.32653 \end{gathered}[/tex]
Hence the answer will be;
[tex]\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}[/tex]
