Math help question: Exponential functions?
A Town with a population of 12,000 has been growing at an average rate of 2.5% for the last 10 years. Assume growth rate will be maintained. The function that models the towns growth is: P(n) = 12(1.025^n) Where P(n) represents population and (n) is the number of years from now. 1. Determine the number of years until the population doubles. 2. Use equation (or other method) to find the number of years ago that the pop. was 8,000. Answer to the nearest year. 3. Determine the population of the town in 10 years. (I got 13,000 something, book said that was wrong) 4. State domain and range of function. I really need help with the first one, I tried subbing in 12,000 for P(n) but I couldn't figure out how to solve for n when its a power. Any help would be really,REALLY appreciated
Math question help, exponential functions?
U.S. health-care expenditures have been growing exponentially during the past two decades. In 2008, expenditures were 2.4 trillion dollars with a growth rate of 9%. Lawmakers hope to decrease the annual growth rate to 2%. Compare the two rates graphically and algebraically as follows. (a) For each growth rate, find an exponential model for the health-care expenditures t years since 2008. f9%(t)= f2%(t)=
Simple Exponential Function???
The concentration of a certain drug in the blood at time t hours after taking the dose is x units, where x = 0.3te^−1.1t. Determine the maximum concentration and the time at which it is reached
Maths Question on Exponential Functions?
The proportion of people responding to a TV advertisement of a new product after it has been on the market for t days is given by : P = 1 - e^-0.2t The marketing area contains 10,000,000 potential customers and each response to the advertisement yields a gross profit of 70 cents (gross profit = sales - cost of good sold). The advertisement costs $30,000 to produce and $5000 for each day it runs. A) Find the value of P when t is very large and interpret its meaning. B)Find an expression for advertising costs over time and hence obtain an expression for net profits over time. (net profit = gross profit - advertising expenses)
What are exponential functions?
Exponential functions are functions of the form f(x) = b^x where b is a constant.The real mathematical importance of exponential functions is in their being proportional to their derivatives meaning the bigger x is, the steeper the slope of the function. This means they grow extremely fast: exponentially fast.A common example of exponential growth is a bacterial population. Since bacteria reproduce rapidly by mitosis, for every bacterium in a culture, there will, before long be two bacteria. Thus, if I have 10 bacteria to start, one minute later I will have 20, and in another minute, each of those twenty will have reproduced and I will have 40; one minute later the same will have happened again and before long, the culture will be overrun with bacteria. The more bacteria there are, the more bacteria there are to make even more bacteria the next minute.All exponential functions are proportional to their derivatives, but the function f(x) = e^x (where e = 2.718281828459…) is actually equal to its derivative meaning the y value of the function at a particular x value is equal to the slope of the curve at that same x value. Thus when dealing with exponential functions in calculus, e becomes a very natural number to use as a base. This is why e is such a big deal and why teachers try to introduce the number early on in Algebra 2, even though it doesn’t have much use at that point in one’s mathematical education.When plotting an exponential curve by hand, one ought to simply pick whole number x values and multiply the base by itself an x number of times to calculate the corresponding y value. This will give a rough plot of the graph of the curve, although a calculator is requires to plot the points not on whole number x values. The curve of simple exponential functions is always increasing and concave up, or vice versa for b^-x. For a positive exponential function like f(x) = e^x, as x approaches ∞, f(x) approaches ∞, and as x approaches -∞, f(x) approaches 0. The curve has no absolute maximum or minimum value and has a horizontal asymptote at y = 0.
Exponential functions simple question please answer?
James bough a car two years ago. The cars value us dispreciating each year. The equation y=17890(.88)^t represents the depreciation in value of the car each year. What is the percent decay rate of the car???
Two PreCalc Questions: exponential functions.?
Ok. There are 2 questions and I have NO idea how to approach them. There doesn't seem to be enough info. The question askes: What is the growth factor? Assume time is measured in the units give. a) water usage is increasing by 3% per year b) a diamond mine is depleted by 1% per day I have the answers for both, (a) is 1.03 per year and (b) is .99 per day but I have NO idea why! Any help please!?
Model Growth Exponential Functions Question(s)?
A=P(1+r/n)^nt is the equation you want to use for exponential equations A= final amount P=initial amount r=rate n=number of times per year t= years P=11.4 million r=0.0163 n=1 t=T - 1997 T= year given in equation a) t=1 and you plug in all the information and get A=11.4*(1+0.0163/1)^1*1 A=11.4*(1+0.0163)^1 A=11.4*(1.0163) A=11.585820 million b)you do the same but for 1999 t=2 and for 2000 t=3 A=11.4*(1+0.0163/1)^2*1 A=11.4*(1+0.0163)^2 A=11.4*(1.0163)^2 A=11.4*1.03286569 A=11.774669 million A=11.4*(1+0.0163/1)^3*1 A=11.4*(1+0.0163)^3 A=11.4*(1.0163)^3 A=11.4*1.049701400747 A=11.966596 million c)for this one just plug in the givens but N= final amount instead of A= final amount N=11.4(1.0163)^t d) use the equation in c and input the years t=8 A=11.4*(1+0.0163/1)^8*1 A=11.4*(1+0.0163)^8 A=11.4*(1.0163)^8 A=11.4*1.13070794607139285950189193752... A=12.890071 million e) with this one you work backwards with N=A=13.6 13.6=11.4(1.0163)^t divide both sides by 11.4 1.192982456...=1.0163^t log 1.192982456... = t (1.0163) t=10 or so so the year is 2007 f) is easy just take N=11.4(1.0163)^t and input the new terms to make it N=No(1+r)^t
What are examples of exponential functions in real life?
Exponential Growth and DecayPutting money in a savings accountThe initial amount will earn interest according to a set rate, usually compounded after a set amount of time. For example, a $2000 deposit, earning .95% interest yearly, will become $2,199 over 10 years. It's small, but it's there.Student fucking loansThe typical student loan has an interest rate between 3 and 4%, so we’ll use 3.75% for a middle that's towards the high end, which is where most of the banks will sit you. This means a $20,000 loan paid off over 10 years will end up costing you $28,900. Woo.Radioactive DecayIn chemistry, radioactive elements break down exponentially, and the decay is shown in terms of half-lives, how long it takes for an element to decay 50%- and this is constant no matter how much of an element there is to begin with. For example, Carbon-14 has a half life of 5,730 years, meaning 100g of carbon will decay to 50g after 5730 years. And after 57,300 years, due to the property of exponential decay, there will still be .097g of carbon in the sample. It will never reach zero. Zeno’s Paradox.[1]Footnotes[1] http://platonicrealms.com/encycl...
A question about the natural exponential function E^x?
The derivative of an exponential function is... f(x)= a^x f'(x) = (ln a)(x')(a^x) the derivative of e^x is, as stated above, simply e^x, and makes the calculation of it's derivative and integrals very simple. It also has a very simple taylor series centered at 0 due to its simple derivative, 1 + x + (x^2)/2! + (x^3)/3!...