For certain decisions, the time it takes to respond is a logarithmic function of the number of choices faced.† One model is given by the following formula where R is the reaction time in seconds and N is the number of choices R = 0.17 + 0.44 log N (c) If the reaction time is to be at most 0.6 second, how many choices can there be? (Round your answer to the nearest whole number.) (d) If the number of choices increases by a factor of 10, what is the difference in the reaction time? (Round your answer to two decimal places.)

What is the carrying capacity for a population modeled by the logistic equation P(t)=250,0001+499e0.45t ? initial population for the model?

Match the exponential function with one of the graphs labeled I,II,III and IV, shown below. (a) f(x)=2x (b) f(x)=2x (c) f(x)=2x (d) f(x)=2x

How is the logarithmic function f(x)=logb(x) related to the exponential function g(x)=bx ? Whatis the result of composing these two functions?

A logistic model is given by the equation S P(t)=901+5e0.42t. To the nearest hundredth, for what value of t does P(t)=45 ?

The formula for measuring sound intensityin decibels D is defined by the equation D=10log(II0) where I is the intensity of the sound in watts persquare meter and I0=1012 is the lowest level of sound that the average person can hear. How manydecibels are emitted from a rock concert with a sound intensity of 4.7101 watts per square meter?

The table shows the mid-year populations (in millions) of five countries in 2015 and the projected populations (in millions) for the year 2025. (a) Find the exponential growth or decay model y=aebt or y=aebt for the population of each country by letting t=15 correspond to 2015. Use the model to predict the population of each country in 2035. (b) You can see that the populations of the United States and the United Kingdom are growing at different rates. What constant in the equation y=aebt gives the growth rate? Discuss the relationship between the different growth rates and the magnitude of the constant.

An investment account was opened with aninitial deposit of 9,600 and earns 7.4 interest,compounded continuously. How much will theaccount be worth after 15 years?

A radiation safety officer is working with 112 grams of a radioactive substance. After 17 days, thesample has decayed to 80 grams. Rounding to fivesignificant digits, write an exponential equationrepresenting this situation. To the nearest day, whatis the half-life of this substance?

Solve: (a) log2(5x1)=6 (b) lne3x=6