Suppose that a volume of air in an air balloon for $$0\ \le\ t\le6$$ is given by the function: $$V\left(t\right)\ =\ 10t\ -\ 2t^2$$ . Is the volume of air increasing or decreasing at t = 2?

The volume of air in the balloon is increasing at t = 2

The volume of air in the balloon is remains the same at t = 2

The volume of air in the balloon is decreasing at t = 2

Suppose that a volume of air in an air balloon for $$0\ \le\ t\le6$$ is given by the function: $$V\left(t\right)\ =\ 10t\ -\ 2t^2$$ . Is the volume of air increasing or decreasing at t = 5 ?

V'(5) = -10, The volume of air in the balloon is decreasing at t=5

V'(5) = 10, The volume of air in the balloon is increasing at t=5

V'(5) = 0, The volume of air in the balloon is not changing at t=5

Suppose that a volume of air in an air balloon for $$0\ \le\ t\le6$$ is given by the function: $$V\left(t\right)\ =\ 10t\ -\ 2t^2$$ . Does the volume of air ever stop changing? If so, when?

The volume of air stops changing at t = 2.5.

The volume of air stops changing at t = 1.5.

The volume of air stops changing at t = 3.5.

A city's population follows the model: $$P\left(t\right)\ =\ 12000e^{\left(0.06t\right)}$$ Where P(t) represents the population after "t" years. Find the rate of population growth after t = 6 years?

$$P$$ This means that after 6 years , the population is increasing at a rate of approximately 1032 people per year .

$$P$$ This means that after 6 years , the population is increasing at a rate of approximately 684 people per year .

$$P$$ This means that after 6 years , the population is increasing at a rate of approximately 872 people per year .

$$P$$ This means that after 6 years , the population is increasing at a rate of approximately 998 people per year .

A bank account earns continuous interest at an annual rate of 6%. The balance is modified by the function: $$A\left(t\right)\ =\ 3000e^{\left(0.08t\right)}$$ Where A(t) represents the account balance after "t" years. Find how fast the account balance is growing after 8 years?

$$A$$ This means that after 8 years , the account balance is increasing at a rate of approximately $455.16 per year .

$$A$$ This means that after 8 years , the account balance is increasing at a rate of approximately $155.16 per year .

$$A$$ This means that after 8 years , the account balance is increasing at a rate of approximately $255.16 per year .

$$A$$ This means that after 8 years , the account balance is increasing at a rate of approximately $ 855.16 per year .

A radioactive substance decays according to the function: $$M\left(t\right)\ =\ 800e^{\left(-0.04t\right)}$$ Where M(t) represents the mass (in grams) remaining after t years. Find the rate at which the substance is decaying after 12 years?

$$M$$ This means that after 12 years , the radioactive substance is decaying at a rate of approximately - 19.80 grams per year . The negative sign indicates decay (decreasing mass over time).

$$M$$ This means that after 12 years , the radioactive substance is decaying at a rate of approximately - 12.80 grams per year . The negative sign indicates decay (decreasing mass over time).

$$M$$ This means that after 12 years , the radioactive substance is decaying at a rate of approximately -8.80 grams per year . The negative sign indicates decay (decreasing mass over time).

$$M$$ This means that after 12 years , the radioactive substance is decaying at a rate of approximately -2.80 grams per year . The negative sign indicates decay (decreasing mass over time).

Calculus 1 Test - Section 2.3 to 2.8: Derivatives of Trig, Exp.

Authored by Joseph Lloyd

Mathematics

12th Grade

CCSS covered

Calculus 1 Test - Section 2.3 to 2.8: Derivatives of Trig, Exp.

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