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

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) Reply

Answer:Step-by-step explanation:knowledgeofpowers of 2, or you can uselogarithmsto find thevalue of t.## Powers of 2

t = 7## Logarithms

t =log(128)/log(2)= 7. . . . . divide by the coefficient of tThe value of t is 7.Additional comment