Answered

Looking for reliable answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Discover reliable solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

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.

__

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)

Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.