🎉 Announcing Numerade's $26M Series A, led by IDG Capital!Read how Numerade will revolutionize STEM Learning Oh no! Our educators are currently working hard solving this question. In the meantime, our AI Tutor recommends this similar expert step-by-step video covering the same topics. Numerade Educator ### Problem 12 Easy Difficulty # The number,$N$, of bacteria in a culture at time$t,$in hours, is$N(t)=1000\left[30+e^{-\frac{1}{5}}\right]$a. What is the initial number of bacteria in the culture?b. Determine the rate of change in the number of bacteria at time$t$.c. How fast is the number of bacteria changing when$t=20 ?$d. Determine the largest number of bacteria in the culture during the interval$0 \leq t \leq 50$.e. What is happening to the number of bacteria in the culture as time passes? ### Answer ## a. 31000b.$-\frac{100}{3} e^{-\frac{1}{6}}$c. -17 bacteria/hd. 31000 at time$t=0\$

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{'transcript': "Okay, So starting off with him to the T equals what girls in e to the corn. Zero won t so for a we're trying to find, But, uh, honey in six or on zero hours. Was this Easter off here? Probably most lovely about me. But how work have nearly e the one girl one plan. Zero goes 1000 when you climbed into the company. So 1000 bacteria, Uh, zero hours. Parents will be. So we're really gonna try to find the girl. Three. So the girl three equals K. No, this is how it look. If we'd been happens, or one day, that's where K would be. Were the ones of the one unlikely. So K equals 10 Why with this And then if you move it twice, see that 1%. So the parole three is 1% right? See, we're trying to see how many insects will be up for hours. So we're gonna plug in for to wear t supposed to be saw. 1000 e 0.1 times for you. Call that in the calculator and you should get 1040.81 in sex up for hours. All right. D um, When will the bacteria reach 1700? Okay, No. Yeah. So 1700 equals album. We're gonna try to see what it was from about 1700. Each of the planes are one t. So we're trying to look for key. So you're going to divide out the 1000 and you should get 1.7 equals e to cleanse Erawan. T you get alone. A lot of seven canceled out the E u left with 0.1 t 2.1 You're left with t equals. Okay, t who's 53.6 hours? It doesn't take a degree. About two hours to reach 17,000 bacteria, not e. Okay, e, we're trying to see the population double. So 1000 twenties to is obviously 2000. You're trying to say when or reach 2000. 2000 equals 1000. You need to the 0.1 t So again, you to buy out the 1000 you can go under knowledgeable, and then you should get two equals e to the point there alone. T you get a loan comes with two crosses out the e and you're left with friends or a woman t tow it off the planes there. One your life with T Ingles. 69.31 hours. So it's gonna take about 69 arms for the population to double."}

University of Houston - Clear Lake

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