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Point) Write the exponential functionS0e 0.17t in the form y ab'Once you have rewritten the formula, give accurate to at least four decimal places_ 0.8437 help...

Question

Point) Write the exponential functionS0e 0.17t in the form y ab'Once you have rewritten the formula, give accurate to at least four decimal places_ 0.8437 help (numbers)is measured in years, indicate whether the exponential function is growing or decaying and find the annual and continuous growth/decay rates_ The rates you determine should be positive in both cases of growth or decay (by choosing decay the negative rate is implied).(b) The annual decayrate15.63% per year (round to the neare

point) Write the exponential function S0e 0.17t in the form y ab' Once you have rewritten the formula, give accurate to at least four decimal places_ 0.8437 help (numbers) is measured in years, indicate whether the exponential function is growing or decaying and find the annual and continuous growth/decay rates_ The rates you determine should be positive in both cases of growth or decay (by choosing decay the negative rate is implied). (b) The annual decay rate 15.63 % per year (round to the nearest 0.01 %). The continuous decay rate is 16.61 % per year (round to the nearest 0.01 %).



Answers

(a) What is the annual percent decay rate for $P=$ $25(0.88)^{t},$ with time, $t,$ in years? (b) Write this function in the form $P=P_{0} e^{k t} .$ What is the continuous percent decay rate?

Were given 1/2 life and were asked to use that to find an exponential decay function. And then the time when 77% of an initial value remains and the time when 6.2% often initial valley remains we'll start by looking at our function were given that the half life so t 1/2 is 5730. We know that the equation is the natural log of two over K. So if we set those equal, then we can solve for this cable you which we don't have. So that's we're looking for here. Okay, we'll be 0.12 and then this is carbon dating is the topic of this. So we're going unused Sea of tea. So the carbon in terms of time is going to be the initial amount times E to the negative K t. We're on. Lee asked about ratios, percentages or ratios of 77 over 106.2 over 100. Right, Since we're only asked about ratios, our initial value isn't gonna matter. So the easiest thing to use will be one. So we're just gonna call it one. This will be E to the negative 0.12 times t. And now I can use that equation to find our answers. So part A is asking for 77% so we can plug this in. So we want to know when 77% of one so 0.77 is going to be equal to e to the negative 0.12 times t were asked about this t value. So we're gonna take the natural log of both sides and then we'll divide by our negative K value here and we'll get that t is equal to 2160 years. And then this is the same process. For part B, we're asked for 6.2% to 6.2% of one is going to be 0.62 That's equal to e to the negative 0.12 times t were asked about this T value will take the natural law Global science and the natural log in the e will cancel and then we'll divide by our negative K value here and we'll get that T is equal to 22,990 years approximately

So this problem is given to us is why equals five times 0.8 to the X power. Okay, so when we're looking for a growth or decay, we just knew Look at what this base is, and that base determines our factor. Um, so if the base is greater than wanted to grow that the base is less than one into decay. So 0.8 is less than one eso This is a decay, okay? And a decay factor. And this is a big thing, So decay factor is equal to the base. Okay, so the decay factor is 0.8 and there is some confusion with this. We'll go ahead and, uh, illustrate if I said what is that it cave rate? So, Dick a ray is how much less than one is it? So, dick, a ray is gonna be one minus. The base came. So even though the answer in this case is 0.8, the decay rate would be 0.2 because it's losing 20% each time. This problem did ask for what is the factor, though? So we're gonna go with 0.8 is the correct answer in this case. Thank you. Very

So we want to start by looking at the function is given to us. P. Equals he not E. To then 0.2 team. And we don't have a specific initial peanut value yet. That's okay then because the way that we write this is we see the E. To the 0.2 T. Is the same thing as E. To the 0.2 times E. To the T. To the way that we're going to end up writing this is um even 0.2 in a pitting 1.2 to 1. So that's what we're going to have. This is going to be P equals key, not times 1.2 to 1 chilukki. It's going to be the same function and we see that this is going to be exponential growth. I'm not only because this was positive, but because now we have this value is greater than one.

Uh huh. Through the given problem, we want to write function. The function is given to us in the form to p equals to eat the negative 0.5 team. And before we look at this graph, we want to consider if it's going to be exponential growth or exponential decay. So the primary way by which we can tell if its growth through decay is based on this X opponent. This is the only way we can know for sure. Um So considering here that we end up having exponential growth here, if this was positive, we know that this is going to be decay because this is negative. So we end up saying that our final answer is that this is going to be exponential decay. So graphing this, we sure enough see that as t increases the function decreases. So you see this is in fact exponential decay.


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