P(t)=30(2)^((t)/( 18)) The function models P, the amount of bacteria, in colony-forming units, in a bacteria culture after t minutes of growth. How many colonyforming units of bacteria are in the bacteria culture after 90 minutes? Choose 1 answer: (A) 3×10^(2) (B) 9.6 ×10^(2) (C) 5.4 ×10^(3) (D) 2.43 ×10^(7)

Question

P(t)=30(2)^((t)/( 18)) The function models  P, the amount of bacteria, in colony-forming units, in a bacteria culture after  t minutes of growth. How many colonyforming units of bacteria are in the bacteria culture after 90 minutes? Choose 1 answer: (A)  3×10^(2) (B)  9.6 ×10^(2) (C)  5.4 ×10^(3) (D)  2.43 ×10^(7)

Bytelearn · Accepted Answer

Identify function and value of t: Identify the given function and the value of t for which we need to find P(t). The function given is P(t) = 30(2)^((t)/(18)), and we need to find the amount of bacteria after t = 90 minutes.Substitute value of t into function: Substitute the value of t into the function to calculate P(90). P(90) = 30(2)^((90)/(18))Simplify the exponent: Simplify the exponent by dividing 90 by 18. (90)/(18) = 5Substitute simplified exponent: Substitute the simplified exponent back into the function. P(90) = 30(2)^5Calculate exponent: Calculate 2 raised to the power of 5. 2^5 = 32Multiply by 30: Multiply the result by 30 to find P(90). P(90) = 30 * 32Perform multiplication: Perform the multiplication to find the number of colony-forming units. P(90) = 960Write final answer in scientific notation: Write the final answer in scientific notation if necessary. 960 can be written as 9.6 × 10^2.

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