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The growth of algae can be modelled by the function f(t) = 2¹.
Find the value of t such that f(t) = 128.

Sagot :

sqdancefan

Answer:

  t = 7

Step-by-step explanation:

You can use your knowledge of powers of 2, or you can use logarithms to find the value of t.

Powers of 2

  2^1 = 2

  2^2 = 4

  2^4 = 16

  128 = 16×4×2 = (2^4)(2^2)(2^1) = 2^(4+2+1) = 2^7

Now, the equation is ...

  f(t) = 2^t = 2^7

Equating exponents, we have ...

  t = 7

Logarithms

Taking the log of both sides of the equation ...

  2^t = 128

we have ...

  t×log(2) = log(128)

  t = log(128)/log(2) = 7 . . . . . divide by the coefficient of t

The value of t is 7.

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Additional comment

The relevant rule of exponents is ...

  (a^b)(a^c) = a^(b+c)

The relevant rule of logarithms is ...

  log(a^b) = b×log(a)

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