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Logarithims and depreciation watch

1. Could someone please take me step by step how on earth I would complete this question:
An asset, A, has a present value of £10000 which depreciates exponentially. The value of the asset at the end of t years is given by y = 10000e-0.12t How many years (to 2dp) will it take for the asset to depreciate down to £3000?
2. I would think you intended to write 'The value of the asset at the end of t years is given by:

as this is the usual form for exponential depreciation.

You know what y is the value after a number of years so if you want to know how long it takes to be valued at £3000 then what you have to do is substitute 3000 in for y so now you have:

Where t is the time taken to depreciate in value to £3000.

All you need to do now is solve it. First divide both sides by 10000 and then remember that if:

then

If it was actually supposed to be

then simply put y as 3000 and then solve the equation.

Hope this helps

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