Expert Answers to Algebra 2 Problems

Determine whether each function is an example of exponential growth or decay. Then find the y-intercept. $y=0.6(1/10{)}^x$

Graph each polynomial function. Estimate the x-coordinate at which the relative maxima and relative minima occur. State the domain and range for each function. $f(x)=-x^3+4x^2-2x-1$

Chance (Fall 2004) published a study on modeling a certain pitch of a musical composition. Data on 147 famous compositions were used to model the number of times (y) a certain pitch occurs called entropy- as a straight-line function of year of birth (x) of the composer. On the basis of the scatterplot of the data, the standard deviation $\sigma \sigma$ of the model is estimated to be $s=.1$. For a given year (x), about 95% of the actual entropy values (y) will fall within d units of their predicted values. Find the value of d.

The following integers should be written using the unique factorization theorem to achieve standard factored form
3675

For the following exercises, consider this scenario: For each year t, the population of a forest of trees is represented by the function $A(t)=115(1.025{)}^t$. In a neighboring forest, the population of the same type of tree is represented by the function ${\displaystyle B\left(t\right)=82{\left(1.029\right)}^t}$. (Round answers to the nearest whole number.) Discuss the above results from the previous four exercises. Assuming the population growth models continue to represent the growth of the forests, which forest will have the greater number of trees in the long run? Why? What are some factors that might influence the long-term validity of the exponential growth model?