Keeper 6 & 7
Rewrite the equation in exponential form.
log(x-4)=5
105=x-4
Rewrite using the change of base formula. DO NOT EVALUATE!
logy45
log45/logy
A new car is purchased for $24,500 dollars. The value of the car depreciates at 7.5% per year using the formula. What will the value of the car be after 8 years? Round your answer to 2 decimal places.
$13131.06
Mandy wants to organize her closet and donate some clothes. She plans to remove one quarter of the clothes in her closet each day. She starts with 100 items of clothing.
What is the average rate of change of the number of items in her closet between 4-7 days?
removes an average of 6 items between days 4 and 7.
The average change in pH can be calculated using the formula, f(x) = log x, where x represents the concentration of hydrogen ions and f(x) represents the pH level of a solution with a certain concentration of hydrogen ions. Find the average change in pH per increase in hydrogen ion concentration over an interval of 4 to 13 moles per liter.
The average change is .06 pH between 4 and 13 moles per liter of hydrogen ions
Rewrite the equation in logarithmic form.
ey+3=14
ln14=y+3
EVALUATE the logarithm using the change of base formula. Round your answer to 2 decimal places.
log213
3.70
Suppose a population of rabbits starts with 5 rabbits and grows at a rate of 15% per year. How long will it take for the rabbit population to reach 70? Use the formula.
18.88 years
Imagine you were modeling the relationship between the distance from a basketball hoop when attempting a shot and the number of shots. Your first shot is 20 feet away and you move a third of the distance to the hoop after each shot.
Find the average distance the ball moves closer to the rim per shot taken over your second and fifth shot.
you move an average of 2.09 feet closer between your second and fifth shot.
Using the function, M = log x, where M is the magnitude of the earthquake and x is the amplitude of the seismic wave, determine how many times greater is the amplitude of an earthquake with a Richter scale rating of 7 as an aftershock with a Richter scale rating of 2?
The difference between the amplitude of Richter scale of 7 and 2 is 105
Find the inverse function for
f(x)=4x+3-6
f-1(x)=log4(x+6)-3
EVALUATE the logarithm using the change of base formula. Round your answer to 2 decimal places.
log398
4.17
Jill deposits $867 into an account that pays 2.36% compounded continuously using the formula f(t)=pert. How much interest will Jill have earned in 4 years?
$952.83
The number of likes on an influencer’s social media post starts with 50 likes and grows exponentially at a rate of 1.2 per hour.
Describe the average number of likes the influencer receives between hours 8 and 11 in context.
there is an average increase of 52 likes per hour between the 8th and 11th hour
Using the formula f(x)=logbx, where f(x) is the decibel level of a sound and x is the intensity of the sound. Determine the base level needed of a sound that is 10 times as intense as a sound with a decibel of 50.
The base level is 1.05
Find the inverse function for
f(x)=log2(x+5)-8
f-1(x)=2x+8-5
Expand the logarithm.
log((x3y8)/s)
3log(x)+8log(y)-log(s)
Determine the initial amount a teacher should invest into an account that pays 3% interest compounded daily if they would like to have $500000 saved for retirement in 30 years. f(t)=p(1+(r/n))nt.
$203292.35
Madison wants to organize her pantry and buy some groceries. She plans to buy one-fifth of additional groceries each day. She starts with 20 items of groceries.
What is the average rate of change of the number of items in her pantry between 2-6 days?
The average number of groceries bought is 8 items between 2 and 6.
Using the equation for loudness L, in decibels, L=10logR, where R is the relative intensity of the sound. If the loudness of the Saturn V launch was 203 decibels, what was the sound's relative intensity?
The sound's relative intensity is 1020.3.
Verifying that f(x) and g(x) are inverses using compositions. Explain how you know!
f(x)=5x-2+4 g(x)=log5(x+2)-4
No, both of the comps. don't equal x (since 2 is always inside and 4 is always outside they can't cancel out or simplify down.)
Simplify the expression to a single logarithm (condense).
5log(x)-(log(y)+3log(r))
log(x5/(yr3))
Kaylee invested $320 in an account paying an interest rate of 4.75% compounded monthly using the formula f(t)=p(1+(r/n))nt. Assuming no deposits or withdraws are made, how much money would be in the account after 12 years? Round to 2 decimal places.
$565.21
The half-life of caffeine is approximately 5 hours; this means that approximately ½ of the caffeine in the bloodstream is eliminated every 5 hours. Suppose you drink a can of Instant Energy, a 16-ounce energy drink that contains 80 mg of caffeine. Suppose the caffeine in your bloodstream peaks at 80 mg.
How much caffeine will remain in your bloodstream after 5 hours?
There will be 40 mg of caffeine in your bloodstream after 5 hours.
Under certain conditions, the wind speed s (in knots) at an altitude of h meters can be modeled by the following function s(h)=2ln(100h). By what amount does the wind speed increase when the altitude quadruples?
The wind speed increases by 2.77 knots.