You deposit

$$\$ 350$$

in an account. The account earns

$$\$ 17.50$$

simple interest in 2.5 years. What is the annual interest rate? The annual interest rate is

Is investing $2000 in an account that pays 5% annual interest compounded continuously the same as investing$1000 at 4% and $1000 at 6%, each compounded continuously? Explain.

Estimate the amount of money you will have in account after $5$ years, assuming that the account earns simple interest. You deposit $\$ 1500$ in an account with an annual interest rate of $4 \%$

A sum of $25000 is deposited in a bank. After 8 years, the simple interest gained was$7000. Calculate the annual rate of interest on the account assuming it remained constant over the 8 years.

A sum of $25 000 is deposited in a bank. After 8 years, the simple interest gained was$7000. Calculate the annual rate of interest on the account assuming it remained constant over the 8 years.

You deposit $500 in a savings account that earns 6% annual interest compounded yearly. Write and solve an exponential equation to determine when the balance of the account will be$800.

A population geneticist is studying the genes found at two different locations on the genome. He estimates the proportion $p_1$ of organisms who have gene A at the first locus to be $\widehat{p}_{1}=0.42$ with uncertainty $\sigma_{1}=0.049.$ He estimates the proportion of organisms that have gene B at a second locus to be $\widehat{p}_{2}=0.23,$ with uncertainty $\sigma_{2}=0.043.$ Under assumptions usually made in population genetics (Hardy–Weinberg equilibrium), $\widehat{p}_{1} \text { and } \widehat{p}_{2}$ are independent and normally distributed, and the proportion p of organisms that have both genes A and B is estimated with $\widehat{p}=\widehat{p}_{1} \widehat{p}_{2}.$ a. Compute $\widehat{p}$ and use propagation of error to estimate its uncertainty. b. Assuming $\widehat{p}$ to be normally distributed, find the P-value for testing $H_{0}: p \geq 0.10.$ c. Generate an appropriate simulated sample of values $\widehat{p}^{*}.$ Is it reasonable to assume that $\widehat{p}$ is normally distributed?

Find the derivative of the logarithmic function. $g(t)=\frac{\ln t}{t^{2}}$

Use Table $3.4$ to answer the following question. Assuming that all prices have risen at the same rate as the CPI. If someone needed $\$ 45,000$ to maintain a certain standard of living in $1996$, how much would be needed to maintain the same standard of living in $2016$?

The table shows the yield y (in milligrams) of a chemical reaction after t minutes.

$$\begin{array}{|l|c|c|c|c|} \hline \text { Minutes, t } & {1} & {2} & {3} & {4} \\ \hline \text { Yield, y} & {1.2} & {7.1} & {9.9} & {13.1} \\ \hline \end{array}$$

$$\begin{array}{|l|c|c|c|c|} \hline \text { Minutes, t} & {5} & {6} & {7} & {8} \\ \hline \text { Yield, y} & {15.5} & {16.0} & {17.9} & {18.0} \\ \hline \end{array}$$

(a) Use the regression capabilities of a graphing utility to find the least squares regression line for the data. Then use the graphing utility to plot the data and graph the model. (b) Use a graphing utility to plot the points (ln t, y). Do these points appear to follow a linear pattern more closely than the plot of the given data in part (a)? (c) Use the regression capabilities of a graphing utility to find the least squares regression line for the points (ln t, y) and obtain the logarithmic model y=a+b ln t. (d) Use a graphing utility to plot the original data and graph the linear and logarithmic models. Which is a better model? Explain.

Refer to the earlier table. Find a logarithmic regression model $(y=a+b \ln x)$ for the total production. Estimate (to the nearest million) the production in 2020.

The table shows the annual revenues R (in billions of dollars) for Amazon.com from 2006 through 2013. (a) Use the regression feature of a graphing utility to find a logarithmic model, an exponential model, and a power model for the data. Let t represent the year, with t = 6 corresponding to 2006. (b) Use the graphing utility to graph each model with the original data. (c) Determine which model best fits the data. Use the model to predict the revenue of Amazon.com in 2019.

Find out the absolute and relative errors in the following situation. The label on a bag of concrete says " $60$ pounds," but the true weight is only $58$ pounds.

Make an order of magnitude estimate of the following quantity. Explain the assumptions you use in your estimates. Total annual spending on movie tickets in the United States