Unit 4 Part 2: Logs Review

Given the logarithmic functions below, order from LEAST to GREATEST in terms of the x-intercepts.

If $$\log_754=x$$ , which of the equations below is the exponential equivalent?

Which expression represents the solution of $$e^{\left(x-3\right)}=6$$

The equation $$25000=20000e^{0.025t}$$ can be solved to determine the time, t, when the population of a city will reach 25000 people.

Find the time. Round to the nearest hundredths.

A scientist is researching how changes in temperature affect specific types of bacteria. The growth of one type of bacteria can be represented by the function $$600=20e^{7t}$$ . Which of these can be used to determine the amount of time in hours, t, that has passed? Select all that apply.

Using a logarithm, solve the following equation for x.

$$36000=\left(200\right)\left(4^{3x}\right)$$
Enter the value for x, rounded to the nearest hundredth.

Five thousand milliliters of bacteria are on a petri dish. The amount, in milliliters, of the substance that is left after t hours can be modeled by the equation $$y=5000e^{-0.0076t}$$ , where y is the amount of the substance left after t hours.

Approximately how many hours will it take unit 60 ml is left?

The graph of a logarithmic function is shown.
Which of the following is the BEST estimate for the rate of change of the function from x=-1 to x=2?

The population of a certain bee colony after t months is modeled by the function $$P\left(t\right)=45\cdot3^t$$ , where $$P\left(t\right)$$ = population in thousands of bees cells. How long will it take the population to reach 900 thousand?

The number of hours it takes for the bee colony population to reach 900 thousand is equal to the logarithm ​ (a)   , which is approximately ​ ​ (b)  

Dayna is looking to invest $30,000 in an investment. She wants to use the money that she invests to pay for a new car that will cost $50,000.

Complete the table to determine how many years, t, it will take for Dayna to increase $30,000 to $50,000 at 3 different interest rates.

Round your answers to the nearest tenth of a year.

If the interest rate is 7%