could u help me? ### Understanding Cell Growth Through Exponential Equations**Description:**A recent scientific study identified nutrient B which helps cells to grow rapidly. Scientists conducting the study forgot to take an initial measurement, but after 3 hours observed that the petri dish contained 80 cells, and after 6 hours the cells had increased to 540. **Objective:**Write an equation that models the number of cells in the dish and fill in the blanks below. You can assume the asymptote is at $ y = 0 $.**Instructions:**1. **Identify the growth parameters:** We need to determine the values of constants $ a $ and $ b $ and the initial number of cells.2. **Formulate the exponential growth equation:** Using the information provided, create the equation.**Given Information:**- After 3 hours: 80 cells- After 6 hours: 540 cells**Formula:**The general form of the exponential growth equation is:\[ y = a \cdot b^t \]Where:- $ y $ is the number of cells at time $ t $- $ a $ is the initial number of cells- $ b $ is the growth factor- $ t $ is the time in hours**Blank Fields:**- The equation will use $ a = $ [type your answer] and $ b = $ [type your answer].- The initial amount in the petri dish was [type your answer] cells.**Steps to Solve:**1. **Find the growth factor $ b $:** - Use the given cell counts at different times to form equations and solve for $ b $. - \[ 80 = a \cdot b^3 \] - \[ 540 = a \cdot b^6 \]2. **Calculate $ a $:** - Solve the equations simultaneously to find the values of $ a $ and $ b $.Submit your answers in the blanks provided in the form above.

Name: could u help me? ### Understanding Cell Growth Through Exponential Equ
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Description: could u help me? ### Understanding Cell Growth Through Exponential Equations**Description:**A recent scientific study identified nutrient B which helps cells to grow rapidly. Scientists conducting the study forgot to take an initial measurement, but

We will find a , b and the initial number of cells in the petri dish as following.

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A recent scientific study identified nutrient B which helps cells to grow rapidly. Scientists conducting the study forgot to take an initial measurement, but after 3 hours observed that the petri dish contained 80 cells, and after 6 hours the cells had increased to540. Write an equation that models the number of cells in the dish and fill in the blanks below. You can assume the asymptote is at y = 0. The equation will use a= type your answer. and b= type your answer. The initial amount in the petri dish was type your answer. cells.

A recent scientific study identified nutrient B which helps cells to grow rapidly. Scientists conducting the study forgot to take an initial measurement, but after 3 hours observed that the petri dish contained 80 cells, and after 6 hours the cells had increased to540. Write an equation that models the number of cells in the dish and fill in the blanks below. You can assume the asymptote is at y = 0. The equation will use a= type your answer. and b= type your answer. The initial amount in the petri dish was type your answer. cells.

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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could u help me?

### Understanding Cell Growth Through Exponential Equations

**Description:**
A recent scientific study identified nutrient B which helps cells to grow rapidly. Scientists conducting the study forgot to take an initial measurement, but after 3 hours observed that the petri dish contained 80 cells, and after 6 hours the cells had increased to 540.

**Objective:**
Write an equation that models the number of cells in the dish and fill in the blanks below. You can assume the asymptote is at $ y = 0 $.

**Instructions:**
1. **Identify the growth parameters:** We need to determine the values of constants $ a $ and $ b $ and the initial number of cells.
2. **Formulate the exponential growth equation:** Using the information provided, create the equation.

**Given Information:**
- After 3 hours: 80 cells
- After 6 hours: 540 cells

**Formula:**
The general form of the exponential growth equation is:
\[ y = a \cdot b^t \]
Where:
- $ y $ is the number of cells at time $ t $
- $ a $ is the initial number of cells
- $ b $ is the growth factor
- $ t $ is the time in hours

**Blank Fields:**
- The equation will use $ a = $ [type your answer] and $ b = $ [type your answer].
- The initial amount in the petri dish was [type your answer] cells.

**Steps to Solve:**
1. **Find the growth factor $ b $:**
- Use the given cell counts at different times to form equations and solve for $ b $.
- \[ 80 = a \cdot b^3 \]
- \[ 540 = a \cdot b^6 \]

2. **Calculate $ a $:**
- Solve the equations simultaneously to find the values of $ a $ and $ b $.

Submit your answers in the blanks provided in the form above.

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