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Problem 104

\(\nabla\) Describe a real-life situation in which a quadratic model would be more appropriate than an exponential model and one in which an exponential model would be more appropriate than a quadratic model.

Expert verified

A quadratic model is more appropriate for modeling the trajectory of a projectile, as its parabolic shape represents the object's motion affected by gravity, initial velocity, and constant acceleration. The equation is \(y(x) = ax^2 + bx + c\). An exponential model is more suitable for population growth, such as bacteria, where the population increases rapidly with each generation. The equation is \(y(x) = A \cdot b^x\), where A is the initial population and b is the growth factor.

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Chapter 9

On the same set of axes, graph \(y=-\ln x, y=A \ln x\), and \(y=A \ln x+C\) for various choices of negative \(A\) and \(C\). What is the effect on the graph of \(y=\ln x\) of multiplying by \(A\) ? What is the effect of then adding \(C\) ?

Chapter 9

Convert the given exponential function to the form indicated. Round all coefficients to four significant digits. $$ f(t)=2.3(2.2)^{t} ; f(t)=Q_{0} e^{k t} $$

Chapter 9

You are trying to determine the half-life of a new radioactive element you have isolated. You start with 1 gram, and 2 days later you determine that it has decayed down to \(0.7\) grams. What is its half-life? (Round your answer to three significant digits.) HINT [First find an exponential model, then see Example 4.]

Chapter 9

Convert the given exponential function to the form indicated. Round all coefficients to four significant digits. $$ f(t)=23.4(0.991)^{t} ; f(t)=Q_{0} e^{-k t} $$

Chapter 9

Simplify: \(e^{\ln x}\).

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