Question

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

Answers

  1. 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.
    __
    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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