+72 The number 'a' represents the number of accounts held in a large advertising firm. The number grows according to the rule: a=75+3t (The 't' is squared/raised), where t is the number of years from the year 2010.
C) How many years will it take for the number of accounts to reach 1000? I've come up with the answer:
75+36(the six is squared)+53675
But it looks wrong and I'm really confused. I'm not asking you to tell me the answer but tell me vaguely how to work it out or what I did wrong. Thanks :)
+33616 If you have \(a=75+3t^2\) and you want to find t when a = 1000, then write
\(1000=75+3t^2\)
Rearrange this to get: \(t^2=\frac{1000-75}{3} \rightarrow t^2=\frac{925}{3}\)
Take the square root: \(t=\sqrt{\frac{925}3{}}\)
+33616 If you mean \(a=75+3^t\) then you get \(3^t=925\)
Here you need to take the logarithm of both sides: \(\ln{3^t}=\ln{925}\)
Now use the property of logarithms that ln mn = n*ln m: \(t\ln3=\ln{925}\)
So \(t=\frac{\ln{925}}{\ln3}\)
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+72 sorry I didn't explain myself properly; When I said the 't' is squared I meant that the 't' is actually raised instead of an actual number. a=75+3t
Sorry, I just literally found out how to make the 't' raised, sorry.
+72 Clearly I'm not a very mathematical person XD
But would you mind explaining what in 925/in 3 means. what does the 'in' bit actually mean?
+33616 You are correct. The ln means the natural logarithm; that is, logarithm to the base e. However you could use logarithm to the base 10 if you prefer (as long as you use the same base for both the 925 and the 3).
(You should find t is just over 6.)
It is NOT "in"!!!!. It is "Ln", which stands for "Natural Log" to base "e=2.718281828..........", instead of "base 10".
