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Problem 70 Medium Difficulty

(a) By graphing $ y = e^{-x/10} $ and $ y = 0.1 $ on a common screen, discover how large you need to make $ x $ so that $ e^{-x/10} < 0.1 $.

(b) Can you solve part (a) without using a graphing device?

Answer

a)
$$
x= 23.026
$$
b)
$$
x > 10 \ln 10
$$

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Video Transcript

this is problem number seventy of this tour. Calculus. Eighth edition, Section two point six Party by graphene Why equals heated the negative x over ten and y equals zero point one on a common screen. Discover how hard you need to make X so that he didn't negative. X Over ten is less than zero point one two three plants, both eating the negative X Horton and zero point one on the scene. The screen and we see the E to the negative X or tendons always created, then zero point one until this point at twenty three point two six for X on the functions change. Oh, are we already? Which one is on top and eat a negative IX over ten is not Weston point one. So the answer based on our ground is approximately twenty three point two six party Kings ho party without using a graphing device. We begin here with the question. When is either the negative six or ten lists and point one? Our first step is to take the reciprocal in in there, we don't have a negative exponent anymore, and since their point one is one of return, they're reciprocal. Would be ten and taking the reciprocal change is a sign of our less than two greeted them. Next we take the natural article times and finally multiply. Write him to both sense. So our final answer is thanks must be greater than ten longer natural Aga ten in under for even the negative X or tend to be less than zero point one and an approximation for ten times Central Bank of ten. Twenty three point Oh two six time We were able to get the same answer. Well, that is interesting device for part me.