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# Exponential model watch

1. An investment bond grows in value according to formula P = Ak^n where A is initial value of bond, k is constant, and P is value of bond after n years,

a) If it is assumed initial investment of £1000 will grow to £3000 in 15 years, find value of k.

Done this part and got k = 1.076 (3 d.p)

b) Show that growth in a) is approximately an annual percentage increase of 7.6%

Seems I've forgotten GCSE stuff and can't do this bit
2. (Original post by G.Y)
An investment bond grows in value according to formula P = Ak^n where A is initial value of bond, k is constant, and P is value of bond after n years,

a) If it is assumed initial investment of £1000 will grow to £3000 in 15 years, find value of k.

Done this part and got k = 1.076 (3 d.p)

b) Show that growth in a) is approximately an annual percentage increase of 7.6%

Seems I've forgotten GCSE stuff and can't do this bit
After 1 year you got . The growth is hence . Out of the initial 1000, this is precisely 0.076, which is 7.6% as a percentage.

Anyway, the whole point of is to scream this at you since the increments are year by year and determines by how much each year it rises. So for you just need the bit after decimal point to determine the percentage increase. For % increase after two years, set and do the same, etc...
3. (Original post by RDKGames)
After 1 year you got . The growth is hence . Out of the initial 1000, this is precisely 0.076, which is 7.6% as a percentage.

Anyway, the whole point of is to scream this at you since the increments are year by year and determines by how much each year it rises. So for you just need the bit after decimal point to determine the percentage increase. For % increase after two years, set and do the same, etc...
How many years do you think is sufficient for proof in the exam?
They can't possibly expect it to be done for all 15 years
4. (Original post by G.Y)
How many years do you think is sufficient for proof in the exam?
They can't possibly expect it to be done for all 15 years
It is sufficient for 1 year. Annually means the increase from one year to the next, and this is governed by for all pairs of years.

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