Logarithms expontential growth decay help

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Halpme9
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Someone pls help me with this question I can’t figure it out because we haven’t being given either k or a
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ghostwalker
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(Original post by Halpme9)
Someone pls help me with this question I can’t figure it out because we haven’t being given either k or a
You're told the value of the car when it's new, i.e. when t=0.

What does k^0 equal?
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Halpme9
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(Original post by ghostwalker)
You're told the value of the car when it's new, i.e. when t=0.

What does k^0 equal?
ah ok its 1 so 12499 = A1 meaning A = 12499 can i apply this to my equation 7000 = AK^36 meaning 7000= 12499K^36
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ghostwalker
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(Original post by Halpme9)
ah ok its 1 so 12499 = A1 meaning A = 12499 can i apply this to my equation 7000 = AK^36 meaning 7000= 12499K^36
Yes.
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Halpme9
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(Original post by ghostwalker)
Yes.
ok thanks after going through with (ii) i didnt get the right answer given what have i done wrong?
7000= 12499k^36
log7000 = log12499k^36
log7000 = 36log12499k
log7000 / 36log12499 = k
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ghostwalker
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(Original post by Halpme9)
ok thanks after going through with (ii) i didnt get the right answer given what have i done wrong?
7000= 12499k^36
log7000 = log12499k^36
log7000 = 36log12499k
log7000 / 36log12499 = k
Forgot your rules of logs

\log Ak^t= \log A +t\log k

Corrected.
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Halpme9
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(Original post by ghostwalker)
Forgot your rules of logs

\log Ak^t= \log A +k\log t
ok i did actually try this but i got lost when i my answer ended up being
k = log 7000 - log 12499 / 36log
i dont know how to divide by 36log?
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ghostwalker
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(Original post by Halpme9)
ok i did actually try this but i got lost when i my answer ended up being
k = log 7000 - log 12499 / 36log
i dont know how to divide by 36log?
Corrected my previous post.

So,

7000=12499 \times k^{36}

Rearrange and taking logs:

\log 7000 - \log 12499 = 36 \log k

And \log k = \dfrac{\log 7000-\log 12499}{36}

Work it out and then take the antilog.
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