PreCalc U5 Test Retake Exponential and Logarithmic Functions

The graph illustrates a logarithmic function of the form y = alog(x). State the domain and range.

• $x\ge0,\ y>a$

• $x\ge0,\ y\in R$

• $x>0,\ y>a$

• $x>0,\ y\in R$

The population of a particular town has been increasing at a rate of 5% per annum. In 2015, the population of the town was 8500. The equation that models the population of the town x years since 2015 is

• y = 8500(5)^x

• y = 8500(1.5)^x

• y = 8500(1.05)^x

• y = 8500(0.05)^x

The value, y, of an investment x years since the initial investment was made is given by y = 1200(1.03)^x . The initial value of the investment, in dollars, was $____.

The value, y, of an investment x years since the initial investment was made is given by y = 1200(1.03)^x . The amount of interest that was earned, after 10 years, to the nearest dollar, was $____.

Select the logarithmic form of  $7^x=y+1$  

•  $\log_7y+1=x$  

•  $\log_7\left(y+1\right)=x$  

•  $\log_xy+1=7$  

•  $\log_x\left(y+1\right)=7$  

Fully expand  $\log\left(\frac{2x}{yz}\right)$  .

•  $\log\left(2\right)+\log\left(x\right)-\log\left(y\right)-\log\left(z\right)$  

•  $\frac{\log\left(2\right)\log\left(x\right)}{\log\left(y\right)\log\left(z\right)}$  

•  $\log\left(2\right)+\log\left(x\right)-\log\left(y\right)+\log\left(z\right)$  

•  $\log\left(2\right)\log\left(x\right)-\log\left(y\right)\log\left(z\right)$  

Fully simplify  $\log_b\left(5m\right)+\log_b\left(2m\right)$  .

•  $\log_b\left(7m\right)$  

•  $\log_b\left(7m^2\right)$  

•  $\log_b\left(10m\right)$  

•  $\log_b\left(10m^2\right)$  

The value of a vehicle, v, can be modelled by the function, v = 32000(0.85)^x, where x represents the number of years since the vehicle was purchased. The value of the vehicle is decreasing at a rate of

• 85% per year

• 15% per year

• 8.5% per year

• 1.5% per year

g(x) = log₄(x-6) + 5. Which of the following statements is false about g^-1(x)?

• The domain of g^-1(x) is (-∞, +∞).

• The range of g^-1(x) is (6, +∞).

• g^-1(x) has an asymptote at y = 5.

• All the statements are true.

Solve

 $34=5\ln\left(x-2\right)$  

• 6.

• 898

• 900

• 902