Check my CALCULUS answers please!

Any short explanation for things I got wrong would be great, too, if possible! Thanks in advanced! :)

8. Which of the following functions grows the fastest?
***b(t)=t^4-3t+9
f(t)=2^t-t^3
h(t)=5^t+t^5
c(t)=sqrt(t^2-5t)
d(t)=(1.1)^t

9. Which of the following functions grows the fastest?
f(t)=2^t-t^3
a(t)=t^5/2
e(t)=e
g(t)=3t^2-t
***b(t)=t^4-3t+9

10. Which of the following functions grows the fastest?
***g(t)=3t^2-t
i(t)=1m(t^100)
e(t)=e
c(t)=sqrt(t^2-5t)
a(t)=t^5/2

11. Which of the following functions grows the slowest?
b(t)=t^4-3t+9
f(t)=2^t-t^3
h(t)=5^t+t^5
***c(t)=sqrt(t^2-5t)
d(t)=(1.1)^t

12. Which of the following functions grows the least?
g(t)=3t^2-t
i(t)=1n(t^100)
e(t)=e
c(t)=sqrt(t^2-5t)
***a(t)=t^5/2

13. Which of the following functions grows the slowest?
j(t)=1/4 1n(t^200)
a(t)=t^5/2
***i(t)=1n(t^100)
g(t)=3t^2-t
b(t)=t^4-3t+9

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  1. exponentials grow faster than powers, and constants don't grow at all(2^x > x^4 > x^5/2 > 10)
    logs grow even slower than roots (since exponentials grow faster than powers): log(x) < √x

    So, in order of increasing growth rate, we have

    #8: c,b,d,f,h
    #9: e,g,a,b,f
    #10: e,i,c,g,a
    #11: c,b,d,f,h
    #12: e,i,c,g,a
    #13: j,a,i,g,b

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  2. Wow... That, just made so much more sense to me with the examples you provided. I'm going to do some more practice questions knowing what you told me. My lesson didn't teach it like you just did!

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  3. I just did some more practice problems, and got them right! Thank you so much! You made my day. :)

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  4. Glad to help.

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