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Exponents and Logarithms · Ages 16–17

Exponential Growth and Decay Practice

Name: Date:

Identify whether each scenario represents growth or decay, write the exponential model y = a(b)^x, and solve for the requested value.

  1. A town with 4,500 residents grows by 5% each year. Identify the initial amount a, the factor b, and write the model for population P(t) after t years.

  2. A new computer bought for $1,200 loses 20% of its value every year. State the decay factor and write the value function V(t).

  3. A savings account starts with $600 and earns 4% interest compounded annually. How much money is in the account after 3 years?

  4. A medication in the bloodstream starts at 250 mg and decreases by 30% each hour. How many milligrams remain after 4 hours? Round to one decimal place.

  5. A sample of 80 yeast cells doubles every 4 hours. Write the function Y(t) in terms of hours t, then calculate the population after 12 hours.

  6. A 100-gram sample of an isotope has a half-life of 6 days. Write the function R(t) and determine how much remains after 18 days.

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Exponential Growth and Decay Practice

Answer key

  1. A town with 4,500 residents grows by 5% each year. Identify the initial amount a, the factor b, and write the model for population P(t) after t years.

    a = 4,500; b = 1.05; Model: P(t) = 4500(1.05)^t

  2. A new computer bought for $1,200 loses 20% of its value every year. State the decay factor and write the value function V(t).

    Decay factor b = 1 - 0.20 = 0.80; Model: V(t) = 1200(0.80)^t

  3. A savings account starts with $600 and earns 4% interest compounded annually. How much money is in the account after 3 years?

    A(3) = 600(1.04)^3 = $674.92

  4. A medication in the bloodstream starts at 250 mg and decreases by 30% each hour. How many milligrams remain after 4 hours? Round to one decimal place.

    M(4) = 250(0.70)^4 = 60.0 mg

  5. A sample of 80 yeast cells doubles every 4 hours. Write the function Y(t) in terms of hours t, then calculate the population after 12 hours.

    Model: Y(t) = 80(2)^(t/4); After 12 hours: Y(12) = 80(2)^(12/4) = 80(2)^3 = 640 cells

  6. A 100-gram sample of an isotope has a half-life of 6 days. Write the function R(t) and determine how much remains after 18 days.

    Model: R(t) = 100(0.5)^(t/6); After 18 days: R(18) = 100(0.5)^(18/6) = 100(0.5)^3 = 12.5 grams