(1) The number of organisms of a certain bacteria at time t can be modeled according to the function N(t) = 2500(1 + 2t²). Find the rate of change of the number.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
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Author:Bruce Crauder, Benny Evans, Alan Noell
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Chapter2: Graphical And Tabular Analysis
Section2.6: Optimization
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Analysis: Real-Ilife Applications
Derivative is defined as the rate of change of a function with respect to a variable.
(1) The number of organisms of a certain bacteria at time t can be modeled according to
the function
N(t) = 2500(1 + 2t?).
Find the rate of change of the number.
(2) A buko pie store can produce buko pie at Php95.00. It is estimated that if the selling price
of the buko pie is x pesos,
then the number of buko pie sold each day is 1000 – x.
a) Express the daily profit of the store as a function of x.
b) Find the derivative of the function formed in part (a).
Hint: Profit = Revenue - Cost
(3) A wire 10 cm long is cut into two pieces, one of length x and the other of length 10 – x.
Each is bent in a shape of a square.
a) Find a function that models the total area enclosed by the two squares as a
function of x.
b) Find the derivative of the function formed in part (a).
Transcribed Image Text:Analysis: Real-Ilife Applications Derivative is defined as the rate of change of a function with respect to a variable. (1) The number of organisms of a certain bacteria at time t can be modeled according to the function N(t) = 2500(1 + 2t?). Find the rate of change of the number. (2) A buko pie store can produce buko pie at Php95.00. It is estimated that if the selling price of the buko pie is x pesos, then the number of buko pie sold each day is 1000 – x. a) Express the daily profit of the store as a function of x. b) Find the derivative of the function formed in part (a). Hint: Profit = Revenue - Cost (3) A wire 10 cm long is cut into two pieces, one of length x and the other of length 10 – x. Each is bent in a shape of a square. a) Find a function that models the total area enclosed by the two squares as a function of x. b) Find the derivative of the function formed in part (a).
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