Continous Growth and Decay. Properties of Logs

Does the model y=500,000e^-.04t model growth or decay?

• Growth

• Decay

Which of the following models would project the value of a company worth $400,000 whose value is continuously decreasing by 8% annually?

• y=400,000e^.08t

• y=400,000e^-.08t

• y=400,000e^-8t

• y=400,000e^8t

A colony of termites is growing continuously at a rate of 6.2% monthly. If the colony starts with 500, how many would there be in one year?

• 1.02 E 35 (huge amount)

• 1052

• 246375

• 532

Jack has a colony of bees. There are 200 bees to start, but the number of bees is growing continuously at a rate of 3.5%. How many bees will there be in 4 hours?

• 236

• 174

• 811

• 230

 Choose the correct expanded common logarithm:

 $\log(4x)$ 

•  $\log4-\log x$  

•  $\log4+\log x$  

•  $4\log x$  

•  $x\log4$  

Choose the correct expanded common logarithm:

 $\log\left(\frac{x}{y}\right)$  

•  $\log x+\log y$  

•  $x\log y$  

•  $\log(x-y)$  

•  $\log x-\log y$  

Choose the correct expanded common logarithm:

 $\log(xy^2)$  

•  $\log x+2\log y$  

•  $\log x+\log y^2$  

•  $\log x-2\log y$  

•  $\log x+\log y+\log2$  

Choose the correctly condensed common logarithm

 $\log x+\log y+3\log z$  

•  $\log\left(xyz^3\right)$  

•  $\log\left(xyz\right)^3\ \ \ \$  

•  $\log\left(3xyz\right)\ \ \ \ \$  

•  $3\log\left(xyz\right)$  

Choose the correctly condensed logarithm

 $2\log_3u-\log_3z$  

•  $2\log_3\left(\frac{u}{z}\right)$  

•  $\log_3\left(\frac{u^2}{z}\right)$  

•  $\log_3\left(u^2-z\right)\ \$  

•  $2\log_3\left(u-z\right)$  

Choose the correct expanded natural logarithm:

 $\ln\left(\frac{8x}{yz}\right)\$  

•  $\ln8+\ln x-\ln y-\ln z$  

•  $\ln8+\ln x-\ln y+\ln z$  

•  $\ln(8x)-\ln(yz)$  

•  $8\ln x-y\ln z$