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13. A lake with a surface area of 60 000 m² has been infected with an invasive algae species. At this moment, the algae take up only 8 m² of the lake's surface, but the area covered by the algae increases constantly. More specifically, the area covered by algae grows by a quarter every week. Let A be the surface of the pond (in m²) that is covered by the algae after t weeks. a. Find an expression for the function A(t). b. How long does it take for the algae to cover the full surface of the lake? c. Make a graph of the function A(t).

13. A lake with a surface area of 60 000 m² has been infected with an invasive algae species. At this moment, the algae take up only 8 m² of the lake's surface, but the area covered by the algae increases constantly. More specifically, the area covered by algae grows by a quarter every week. Let A be the surface of the pond (in m²) that is covered by the algae after t weeks. a. Find an expression for the function A(t). b. How long does it take for the algae to cover the full surface of the lake? c. Make a graph of the function A(t).

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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13. A lake with a surface area of 60 000 m² has been infected with an invasive algae species. At this moment, the algae take up only 8 m² of the lake's surface, but the area covered by the algae increases constantly. More specifically, the area covered by algae grows by a quarter every week. Let A be the surface of the pond (in m²) that is covered by the algae after t weeks. a. Find an expression for the function A(t). b. How long does it take for the algae to cover the full surface of the lake? c. Make a graph of the function A(t). d. Now make a graph of the function A(t) with a logarithmic scale on the vertical axis and a normal scale on the horizontal axis. What do you notice? Explain!
Transcribed Image Text:13. A lake with a surface area of 60 000 m² has been infected with an invasive algae species. At this moment, the algae take up only 8 m² of the lake's surface, but the area covered by the algae increases constantly. More specifically, the area covered by algae grows by a quarter every week. Let A be the surface of the pond (in m²) that is covered by the algae after t weeks. a. Find an expression for the function A(t). b. How long does it take for the algae to cover the full surface of the lake? c. Make a graph of the function A(t). d. Now make a graph of the function A(t) with a logarithmic scale on the vertical axis and a normal scale on the horizontal axis. What do you notice? Explain!
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