What is the value of $$y=3(2)^x$$ when $$x=5$$ ?

When $$x=5$$ , $$y=3(2)^5 = 3(32) = 96$$ .

What is the initial value in the function $$f(h) = 6(3)^h$$ ?

The initial value in the function $$f(h) = 6(3)^h$$ is 6, which represents the number of cells at time $$h=0$$ .

How do you find the number of cells after a certain number of hours if they triple every hour?

To find the number of cells after $$h$$ hours, use the formula $$f(h) = N_0 \times 3^h$$ , where $$N_0$$ is the initial number of cells.

What is the formula for continuous compound interest?

The formula for continuous compound interest is $$A = Pe^{rt}$$ , where $$A$$ is the amount of money accumulated after time $$t$$ , $$P$$ is the principal amount, $$r$$ is the annual interest rate, and $$e$$ is Euler's number.

What is the common ratio in a geometric sequence?

The common ratio in a geometric sequence is the factor by which each term is multiplied to get the next term. It is found by dividing any term by the previous term.

How do you model a situation where a quantity decreases by a percentage?

To model a situation where a quantity decreases by a percentage, use the formula $$N(t) = N_0(1 - r)^t$$ , where $$N_0$$ is the initial quantity, $$r$$ is the rate of decrease, and $$t$$ is time.

What is the significance of the base in an exponential function?

The base in an exponential function determines the rate of growth or decay. A base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

How do you evaluate an exponential function at a given point?

To evaluate an exponential function at a given point, substitute the value of $$x$$ into the function and calculate the result.

What is the general form of an exponential decay function?

The general form of an exponential decay function is $$f(t) = N_0 e^{-kt}$$ , where $$N_0$$ is the initial amount, $$k$$ is the decay constant, and $$t$$ is time.

Algebra I - Topic 6 Review Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is an exponential function?

Back

2.

FLASHCARD QUESTION

Front

How do you determine if a sequence is geometric?

Back

A sequence is geometric if the ratio of consecutive terms is constant. This means that each term can be obtained by multiplying the previous term by a fixed, non-zero number.

3.

FLASHCARD QUESTION

Front

What is the formula for exponential growth?

Back

4.

FLASHCARD QUESTION

Front

What is the difference between exponential growth and linear growth?

Back

Exponential growth increases at a rate proportional to its current value, leading to faster increases over time, while linear growth increases by a constant amount.

5.

FLASHCARD QUESTION

Front

How do you write an exponential function for an investment?

Back

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

What does it mean for a function to triple every hour?

Back

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