Exponential & Logarithmic Functions Review

Select the characteristics of the equation of the graph shown.

• Exponential function with b>1

• Exponential function with 0<b<1

• Logarithmic function with a>0

• Logarithmic function with a<0

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 $____.

Suppose that the value of an investment, y, can be represented by y = 1000(1.08)^x, where x represents the number of years since the investment was made. Write a function that would model the situation where the initial investment was only half of what it was for the one described by the equation y = 1000(1.08)^x.

• y = 1000(1.04)^x

• y = 500(1.04)^x

• y = 500(1.08)^x

• y = 500(0.54)^x

Which of the following could represent a correct step in the algebraic solution to  $8^{3x}=4^{2x-1}$  ?

•  $4^{6x}=4^{2x-1}$  

•  $2^{9x}=2^{4x-1}$  

•  $2^{9x}=2^{4x-2}$  

•  $2^{12x}=2^{4x-2}$  

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

•  $\log_7y+1=x$  

•  $\log_7\left(y+1\right)=x$  

•  $\log_xy+1=7$  

•  $\log_x\left(y+1\right)=7$  

Select the exponential form of  $2\log_my=n$  

•  $y^2=m^n$  

•  $2y=m^n$  

•  $y^2=n^m$  

•  $2y=n^m$  

When log(4) - 3log(2) + log(5) is expressed as a single logarithm, it can be written as log(a). The value of a is ____.