Understanding exponential growth and decay models:

• What is the formula for exponential growth?

  $y =$$Ce^(kt)$
• What does the variable `y` represent in the exponential growth formula?

  Quantity at time `t`
• In exponential decay, the decay constant `k` must be positive.

  True
• The formula for exponential growth remains the same regardless of the quantity being modeled.

  True
• What is the formula for exponential decay?

  $y =$$Ce^( - kt)$
• In the exponential decay formula, `k` is called the decay constant
• The differential equation for exponential growth is `dy/dt = ky`.


  True
• Match the differential equation with its model:

  $dy / dt =$$ky$ ↔️ Growth

  $dy / dt =$$- ky$ ↔️ Decay
• In the decay model `dy/dt = -ky`, the constant `k` is positive.


  True
• Steps to calculate the growth/decay rate `k` for an exponential model:

  1️⃣ Identify initial quantity `C` and final quantity `y` at time `t`

  2️⃣ Use the formula for growth or decay to find `k`
• What is the growth rate of a bacteria population that grows from 500 to 1200 in 3 hours?

  0.29
• What is the decay rate of a substance that reduces from 300 grams to 150 grams in 8 days?

  0.087
• What does the growth constant `k` represent in exponential growth?

  Rate of increase
• What is the formula for exponential decay?

  y = Ce^(-kt)
• What is the formula for a radioactive substance decaying at 5% per year if its initial mass is 100 grams?

  y = 100e^(-0.05t)
• The formula to find `k` for exponential decay is `k = (ln(y/C)) / t`.

  False
• A bacteria population grows from 500 to 1200 in 3 hours. What is the growth rate `k`?

  0.29
• The formula for exponential decay is `k = (ln(y/C)) / t`

  False
• What is the general solution for the differential equation `dy/dt = ky` in exponential growth?

  $y =$$Ce^{kt}$
• What is the solution to the differential equation `dy/dt = -ky` for exponential decay?

  $y =$$Ce^{ - kt}$
• Suppose a population starts at 100 cells and grows at 20% per hour. What is the expression for `y` at time `t`?

  $y =$$100e^{0.2t}$
• What is the formula used to model population growth?

  $P(t) =$$P_{0}e^{kt}$
• In the exponential growth formula, `C` represents the initial quantity
• In the exponential growth formula, `t` represents the time elapsed
• What does the variable `C` represent in the exponential decay formula?

  Initial quantity
• What does the variable `y` represent in the exponential growth formula?

  Quantity at time `t`
• The decay constant `k` in exponential decay must be positive.


  True
• What does the variable `y` represent in the exponential decay formula?

  Quantity at time `t`
• The differential equation for exponential decay is `dy/dt = -ky
• What do the differential equations for exponential growth and decay express?

  Rate of change
• What is the differential equation for a population growing at 2% per year if it starts at 1000?

  dy/dt = 0.02y
• For exponential growth, the formula to find `k` is `k = (ln(y/C)) / t
• The growth/decay rate is a percentage per unit time
• Exponential growth occurs when a quantity increases at a constant rate.

  False
• A bacteria population doubles every hour. What is the growth constant `k` for this scenario?

  ln(2)
• In the exponential decay formula `y = Ce^(-kt)`, the variable `C` represents the initial quantity
• Match the differential equation with its description:

  `dy/dt = ky` ↔️ Growth

  `dy/dt = -ky` ↔️ Decay
• What formula is used to calculate the growth rate `k` if `y = Ce^(kt)`?

  k = (ln(y/C)) / t
• What is the differential equation for a population growing at 2% per year from an initial size of 1000?

  $\frac{dy}{dt} =$$0.02y$
• What does `y` represent in the growth/decay rate formulas?

  Final quantity