11.5 (Growth and Decay)

Question 1

What is an exponential growth model describe?

Answer 1

Exponential growth describes how a quantity increases over time at a rate proportional to its current size.

Question 2

What is k like for an exponential growth model?

Answer 2

k>0

Question 3

What is the solution to the exponential growth equation
𝑑𝑦/𝑑𝑡=𝑘𝑦

Answer 3

y(t)=y0e^(kt)

Question 4

what do y0 and k represent in the exponential growth or decay formula?

Answer 4

where 𝑦 0is the initial amount at 𝑡=0 k is the growth or decay constant.

Question 5

What does the exponential decay model describe?

Answer 5

Exponential decay describes how a quantity decreases over time at a rate proportional to its current size

Question 6

What is k like for an exponential decay model?

Answer 6

where k<0.

Question 7

What is the solution to the exponential decay equation 𝑑𝑦/𝑑𝑡=-ky

Answer 7

y0e^(−kt)?

Question 8

How do you find k if given data points?

Answer 8

Use the equation y(t)=y0e^(kt) and substitute the given values to solve for 𝑘

Question 9

What is the half-life in exponential decay?

Answer 9

The half-life is the time required for a quantity to decay to half its initial amount.

Question 10

What is the formula for the half-life in exponential decay?

Answer 10

t 1/2=ln(2)/k

Question 11

How do you apply an initial condition in growth and decay problems?

Answer 11

Substitute the initial condition (e.g.,
y(0)=y0into the equation to solve for constants like y0

Question 12

What is the doubling time in exponential growth?

Answer 12

The doubling time is the time it takes for a quantity to double.

Question 13

What is the formula for doubling time in exponential growth?

Answer 13

tdouble=ln(2)/k

Question 14

What does each term in the function y(t)=y0^e^(kt) describe in real-world terms?

Answer 14

It describes a quantity y growing or decaying over time t, starting with an initial amount 𝑦0, at a rate k.