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inn [45]
3 years ago
6

The amount Troy charges to mow a lawn is proportional to the time it takes him to mow the lawn. Troy charges $30 to mow a lawn t

hat took him 1.5 hours to mow. Which equation models the amount in dollars, d, Troy charges when it takes him h hours to mow a lawn?
Mathematics
2 answers:
kati45 [8]3 years ago
8 0
The answer is d=20h

Hope this helps, please brainliest, If u can <33
Strike441 [17]3 years ago
6 0

Answer:

20

Step-by-step explanation:

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The number of bacteria after t hours is given by N(t)=250 e^0.15t a) Find the initial number of bacteria and the rate of growth
Art [367]

Answer:

a) N_0=250\; k=0.15

b) 334,858 bacteria

c) 4.67 hours

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Step-by-step explanation:

a) Initial number of bacteria is the coefficient, that is, 250. And the growth rate is the coefficient besides “t”: 0.15. It’s rate of growth because of its positive sign; when it’s negative, it’s taken as rate of decay.

Another way to see that is the following:

Initial number of bacteria is N(0), which implies t=0. And N(0)=N_0. The process is:

N(t)=250 e^{0.15t}\\N(0)=250 e^{0.15(0)}\\ N_0=250e^{0}\\N_0=250\cdot1\\ N_0=250

b) After 2 days means t=48. So, we just replace and operate:

N(t)=250 e^{0.15t}\\N(48)=250 e^{0.15(48)}\\ N(48)=250e^{7.2}\\N(48)=334,858\;\text{bacteria}

c) N(t_1)=4000; \;t_1=?

N(t)=250 e^{0.15t}\\4000=250 e^{0.15t_1}\\ \dfrac{4000}{250}= e^{0.15t_1}\\16= e^{0.15t_1}\\ \ln{16}= \ln{e^{0.15t_1}} \\  \ln{16}=0.15t_1 \\ \dfrac{\ln{16}}{0.15}=t_1=4.67\approx 5\;h

d) t_2=?\; (N_0→3N_0 \Longrightarrow 250 → 3\cdot250 =750)

N(t)=250 e^{0.15t}\\ 750=250 e^{0.15t_2} \\ \ln{3} =\ln{e^{0.15t_2}}\\ t_2=\dfrac{\ln{3}}{0.15} = 2.99 \approx 3\;h

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prisoha [69]

Okay, so first off, if you need to graph anything, I suggest Desmos, it's a website with an online graphing calculator. It saved my life for highschool geometry.

Now, to answer your question, your y-intercept is going to be at point (0,2). Your x-intercepts are going to be at points (-2,0) and (-4,0). Your point is at (-3,-1). And then your lines simply extend from there.

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