Flnd theisolution oftha exponential equation In Exampla (Enler Your answicrs 05 comma:scparaled Ilec.[0/1 Points]DETAILSPREVIOUS ANSWERSSCOLALG? 4.5.050. 3/5 Submis...

For the following exercises, solve each equation by rewriting the exponential expression using the indicated logarithm. Then use a calculator to approximate the variable to 3 decimal places.
$50 e^{-0.12 t}=10$ using the natural log

All right. Wrong question. 3 62 Problem. Asked us to solve using natural walk. Okay, first thing we're gonna do is divide both sides by 50. That's gonna give us E to the negative. 0.12 T is equal to 0.2. Okay. Hey, Maciste used natural log. So natural log of E to the negative 0.12 Tea is equal to natural log. Uh, 0.2. We know that natural log and either xar inverse operations of each other. So that's gonna leave us with negative 0.12 t is equal to the natural law of 0.2 and we can go ahead and divide both sides by negative as you're a point, too. To be left with tea, um, is equal to this is I wrote, um, several places behind the desk mole. Just because I cannot say that on the calculator I was using and I wanted to make sure that I got the right answer. So I did write lots of decimal places there. You don't want around too. Too early because then Ah, a couple of your decimal place starting to be off, so I did write several places, but if your calculator saves that number for you, that's perfect. Just save it. Divided by negative 0.2. So we get approximately 13.412 for our value of teeth.

Okay, so we want to solve the falling using our natural law. So let's start by dividing by 50 humble of science. So we get a 1/5 and once we've isolated r E, we can now take the natural laudable sides to bring down or power. Okay, so we get negative. Important still wants you to. And then we have the natural rugby. But that's difficult to one. Okay, now let's divide both sides by negative 0.12 to get the T is equal to the natural log of 1/5, all over the good of 0.12

Uh Ready? We have 50 divided by one minus two E. Raised to the negative 0.1 X. Equals 1000. Mhm. All right. So I'm gonna cross multiply because my variables in the denominator and I want to get it to the numerator. So I have 1000 time is one minus two E. To the negative zero 0.1 X equals 50. Now I'm going to divide both sides by 1000. Yes. And I have one minus two E. Raised to the negative zero point 001 X. Equals 1/20. Um Next I want to subtract one. So now I have negative two E. Raised to the negative 0.1 X equals 1/20 minus one is negative. And 19/20 I'm going to multiply both sides by the reciprocal of negative two which is negative one half. Which is the same as dividing by negative two. So then this becomes a positive 19/40 equals E. To the negative zero 0.1 X. Taking the natural log of both sides. I get I admit, yep married, I'm good. I get negative 0.1 X. Natural log of E equals natural log 19/40. Natural beauty is one. So I have negative 0.1 X equals the natural log of 19/40. And then I divide by negative 0.1 Okay. And X will equal. So I have to take I'm gonna do that in two steps. Uh Natural log 19 divided by 40 is negative seven point negative 0.7444 divided by negative 0.1 moves the decimal. So we have positive 744 0.440

We have to solve the exponential equation Aljabr equally and round the result to three decimal places and the question is 50. Divide by one minus two e to the power minus 0.1 X is equal to 1000. No use Negative father rule we get 50 are born one minus two. Divide by E to the power 0.1 Eggs is equal to 1000 now multiply both sides by one minus two. Divide by E to the power 0.1 x we get 50 is equal to 1000 multiply way one minus two Divide by U to the power 0.1 x Divide both sides by 1000 We get wanna born 20 is equal to one minus two Divide by E to the power 0.1 Eggs now subject one from vote site and we get one upon 20 minus one is equal to minus two upon e toda power 0.1 x Now we have minus 19 upon 20 is equal to minus two upon e to the power 0.1 x multiply both sides by E to the power zero point 001 x we get minus 19 are born doing diy E to the power 0.1 x is equal to minus two. Now multiply both sides by doing B. We get minus 19 e to the power 0.1 X is equal to minus 40. Now divide vote sites by minus 19. We get e toda power 0.1 x his equality 40 upon 19 Now use definition off natural log we get 0.1 X is equal to log 40 upon 19 now divide both sides by 0.1 we get X is equal to log 40 Be right by 0.1 log 19 and we get value off X is equal to 7 44.440 This is answer