Continuous compounding is the mathematical limit that compound interest can reach.
It is the limit of the function A(1 + 1/n) ^ n as n approaches infinity. IN theory interest is added to the initial amount A every infinitesimally small instant.
The limit of (1 + 1/n)^n is the number e ( = 2.718281828 to 9 dec places).
Say we invest $1000 at daily compounding at yearly interest of 2 %. After 1 year the $1000 will increase to:-
1000 ( 1 + 0.02/365)^365 = $1020.20
with continuous compounding this will be
1000 * e^1 = $2718.28
The difference between the smoker and the non-smoker is $151
1000 x $7.85 = $785
1000 x $9.36 = $936
= $151
It is 12 (explanation: unit rate is per unit so 16/16 mile or 1 mile = x minutes so if you multiple 1/16 by sixteen and do the same on the other side (3/4 times 16), you get 20 (hope this helps!)
The slope is 1 :)
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