**Problem Statement:**Cara tracked the population of fish in a pond. At the end of the first year, she counted 8 fish. Over the years, the population tripled each year.**Question:**Which equation can be used to determine the number of fish, $ f $, after $ t $ years?**Options:**A. $ f = 3 \cdot 8^{(t-1)} $B. $ f = 3 \cdot 8^t $C. $ f = 8 \cdot 3^t $D. $ f = 8 \cdot 3^{(t-1)} $ *(selected option)***Explanation:**- The initial population of fish is 8.- The population triples every year.Since the population starts with 8 fish and triples each subsequent year, the correct equation to model this growth pattern is:\[ f = 8 \cdot 3^{(t-1)} \]This equation accounts for the initial count of 8 fish and multiplies by 3 raised to the power of $(t-1)$, representing the tripling effect after the first year.

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Cara tracked the population of fish in a pond. At the end of the first year, she counted 8 fish. Over the years, the population tripled each year. Which equation can be used to determine the number of fish, f, after t years? Af=3.8(t-1) f=3.8t CO f=8.3t Do f=8.3(t-1)

Cara tracked the population of fish in a pond. At the end of the first year, she counted 8 fish. Over the years, the population tripled each year. Which equation can be used to determine the number of fish, f, after t years? Af=3.8(t-1) f=3.8t CO f=8.3t Do f=8.3(t-1)

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

**Problem Statement:**

Cara tracked the population of fish in a pond. At the end of the first year, she counted 8 fish. Over the years, the population tripled each year.

**Question:**

Which equation can be used to determine the number of fish, $ f $, after $ t $ years?

**Options:**

A. $ f = 3 \cdot 8^{(t-1)} $

B. $ f = 3 \cdot 8^t $

C. $ f = 8 \cdot 3^t $

D. $ f = 8 \cdot 3^{(t-1)} $ *(selected option)*

**Explanation:**

- The initial population of fish is 8.
- The population triples every year.

Since the population starts with 8 fish and triples each subsequent year, the correct equation to model this growth pattern is:

\[ f = 8 \cdot 3^{(t-1)} \]

This equation accounts for the initial count of 8 fish and multiplies by 3 raised to the power of $(t-1)$, representing the tripling effect after the first year.

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