Math / Algebra

QuestionIn the model for exponential growth or decay, the amount, or size, at t = 0 is represented by $\qquad$ - The amount, or size, at time $t$ is represented by $\qquad$ - $\qquad$ In the model for exponential growth or decay, the amount, or size, at $t=0$ is represented by $\square$ The amount, or size, at time $t$ is represented by $\square$ k. $A_{0}$ 。 e. t.

Studdy Solution

STEP 1

What is this asking? This problem wants us to identify what different parts of the exponential growth/decay formula represent. Watch out! Don't mix up the initial amount and the amount at time $t$ .
Also, remember that $e$ and $k$ have special meanings!

STEP 2

1. Understand the formula
2. Identify the initial amount
3. Identify the amount at time $t$

STEP 3

Let's break down the exponential growth/decay formula.
It's usually written like this: $A(t) = A_0 \cdot e^{kt}$ .
This formula tells us how a quantity changes over time.

STEP 4

$A(t)$ represents the amount of something at a specific time, $t$ .
Think of it like this: if you're growing bacteria in a dish, $A(t)$ is the number of bacteria you have after a certain amount of time has passed.

STEP 5

$A_0$ is the initial amount.
It's what you start with at time $t = 0$ .
In our bacteria example, $A_0$ is the number of bacteria you put in the dish at the very beginning.

STEP 6

$k$ is the growth or decay constant.
It tells us how fast the quantity is growing or decaying.
A positive $k$ means growth, and a negative $k$ means decay.

STEP 7

Finally, $e$ is just a special number, approximately equal to 2.718.
It's called Euler's number, and it's super important in all sorts of math and science!

STEP 8

The initial amount, or the amount at $t = 0$ , is represented by $A_0$ .
Remember, this is what we start with.

STEP 9

The amount at any given time $t$ is given by $A(t)$ .
This is the value we get after letting our initial amount grow or decay for a certain amount of time.

STEP 10

The amount at $t = 0$ is represented by $A_0$ .
The amount at time $t$ is represented by $A(t)$ .

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Studdy Solution

STEP 1

What is this asking? This problem wants us to identify what different parts of the exponential growth/decay formula represent. Watch out! Don't mix up the initial amount and the amount at time $t$ .
Also, remember that $e$ and $k$ have special meanings!

STEP 2

1. Understand the formula
2. Identify the initial amount
3. Identify the amount at time $t$

STEP 3

Let's break down the exponential growth/decay formula.
It's usually written like this: $A(t) = A_0 \cdot e^{kt}$ .
This formula tells us how a quantity changes over time.

STEP 4

$A(t)$ represents the amount of something at a specific time, $t$ .
Think of it like this: if you're growing bacteria in a dish, $A(t)$ is the number of bacteria you have after a certain amount of time has passed.

STEP 5

$A_0$ is the initial amount.
It's what you start with at time $t = 0$ .
In our bacteria example, $A_0$ is the number of bacteria you put in the dish at the very beginning.

STEP 6

$k$ is the growth or decay constant.
It tells us how fast the quantity is growing or decaying.
A positive $k$ means growth, and a negative $k$ means decay.

STEP 7

Finally, $e$ is just a special number, approximately equal to 2.718.
It's called Euler's number, and it's super important in all sorts of math and science!

STEP 8

The initial amount, or the amount at $t = 0$ , is represented by $A_0$ .
Remember, this is what we start with.

STEP 9

The amount at any given time $t$ is given by $A(t)$ .
This is the value we get after letting our initial amount grow or decay for a certain amount of time.

STEP 10

The amount at $t = 0$ is represented by $A_0$ .
The amount at time $t$ is represented by $A(t)$ .

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Studdy Solution

STEP 1

What is this asking? This problem wants us to identify what different parts of the exponential growth/decay formula represent. Watch out! Don't mix up the **initial amount** and the **amount at time** ttt.Also, remember that eee and kkk have special meanings!

STEP 2

1. Understand the formula2. Identify the initial amount3. Identify the amount at time ttt

STEP 3

Let's break down the exponential growth/decay formula.It's usually written like this: A(t)=A0⋅ektA(t) = A_0 \cdot e^{kt}A(t)=A0​⋅ekt.This formula tells us how a quantity changes over time.

STEP 4

A(t)A(t)A(t) represents the amount of something at a specific time, ttt.Think of it like this: if you're growing bacteria in a dish, A(t)A(t)A(t) is the number of bacteria you have after a certain amount of time has passed.

STEP 5

A0A_0A0​ is the **initial amount**.It's what you start with at time t=0t = 0t=0.In our bacteria example, A0A_0A0​ is the number of bacteria you put in the dish at the very beginning.

STEP 6

kkk is the **growth or decay constant**.It tells us *how fast* the quantity is growing or decaying.A positive kkk means growth, and a negative kkk means decay.

STEP 7

Finally, eee is just a special number, approximately equal to **2.718**.It's called **Euler's number**, and it's super important in all sorts of math and science!

STEP 8

The **initial amount**, or the amount at t=0t = 0t=0, is represented by A0A_0A0​.Remember, this is what we *start* with.

STEP 9

The amount at any given time ttt is given by A(t)A(t)A(t).This is the value we get after letting our **initial amount** grow or decay for a certain amount of time.

STEP 10

The amount at t=0t = 0t=0 is represented by A0A_0A0​.The amount at time ttt is represented by A(t)A(t)A(t).

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

What is this asking? This problem wants us to identify what different parts of the exponential growth/decay formula represent. Watch out! Don't mix up the initial amount and the amount at time $t$ .
Also, remember that $e$ and $k$ have special meanings!

1. Understand the formula
2. Identify the initial amount
3. Identify the amount at time $t$

Let's break down the exponential growth/decay formula.
It's usually written like this: $A(t) = A_0 \cdot e^{kt}$ .
This formula tells us how a quantity changes over time.

$A(t)$ represents the amount of something at a specific time, $t$ .
Think of it like this: if you're growing bacteria in a dish, $A(t)$ is the number of bacteria you have after a certain amount of time has passed.

$A_0$ is the initial amount.
It's what you start with at time $t = 0$ .
In our bacteria example, $A_0$ is the number of bacteria you put in the dish at the very beginning.

$k$ is the growth or decay constant.
It tells us how fast the quantity is growing or decaying.
A positive $k$ means growth, and a negative $k$ means decay.

Finally, $e$ is just a special number, approximately equal to 2.718.
It's called Euler's number, and it's super important in all sorts of math and science!

The initial amount, or the amount at $t = 0$ , is represented by $A_0$ .
Remember, this is what we start with.

The amount at any given time $t$ is given by $A(t)$ .
This is the value we get after letting our initial amount grow or decay for a certain amount of time.

The amount at $t = 0$ is represented by $A_0$ .
The amount at time $t$ is represented by $A(t)$ .