Oil Consumption The rate of consumption of oil (in billions...

Oil Consumption The rate of consumption of oil (in billions of barrels) by the company in Exercise 71 was given as $$1.2e^{0.04}$$ where $t=0$ corresponds to $2010 .$ Find the total amount of oil used by the company from 2010 to year $T .$ At this rate, how much will be used in 5 years? YOUR TURN ANSWERS 1. 26 $\quad$ 2. 256$\quad$ 3. 2 $\ln 3$ or $\ln 9$ 4. 128$/ 3 \quad$ 5. 54

Oil Consumption The rate of consumption of oil (in billions of barrels) by the company in Exercise 71 was given as
$$1.2e^{0.04}$$
where $t=0$ corresponds to $2010 .$ Find the total amount of oil used by the company from 2010 to year $T .$ At this rate, how much will be used in 5 years?
YOUR TURN ANSWERS
1. 26 $\quad$
2. 256$\quad$
3. 2 $\ln 3$ or $\ln 9$
4. 128$/ 3 \quad$
5. 54

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Key Concepts

Definite Integral for Accumulation

The definite integral is used to calculate the total accumulation of a quantity over a given interval. When a rate function is integrated with respect to time, the result is the total amount (or accumulation) of the quantity from the starting time to the ending time.

Integration of Exponential Functions

This is a specific integration technique where the integral of an exponential function is computed. Understanding the antiderivative of an exponential function is crucial for evaluating the definite integrals that appear in accumulation problems.

Exponential Growth Model

This concept involves modeling a quantity that increases (or decreases) at a rate proportional to its current amount. In many real?world applications, including consumption or population models, the growth or decay is represented by an exponential function, where the constant in the exponent determines the rate of change.

Rate Function

A rate function describes the instantaneous change of a quantity with respect to time. In problems like this, the rate function is given by an exponential expression and signifies how fast the oil is being consumed at any moment.

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