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Newton's law of cooling indicates that the temperature of a warn object will decrease exponentially with time and will approach the temperature of the surrounding air. The temperature T(t) is modeled by $T (t) = T_{a} + (T_{0} - T_{a}) e^{- k t}$ . In this model, $T_{a}$ represents the temperature of the surrounding air, $T_{0}$ represents the initial temperature of the object and t is the time after the object starts cooling. The value of k is the cooling rate and is a constant related to the physical properties the object.
A cake comes out of the oven at 335F and is placed on a cooling rack in a 70F kitchen. After checking the temperature several minutes later, it is determined that the cooling rate k is 0.050. Write a function that models the temperature T(t) of the cake t minutes after being removed from the oven.

CheemnCatelvew 2021-02-09

In 2015, there were 3,600 people living in a small town. Every year, the population grows by 4.5%. Write the exponential equation that represents the town's population t years from now, in 2015. Then, how about using your equation to predict the population in 2025?

glamrockqueen7 2021-02-09

The table gives the number of active Twitter users worldwide, semiannually from 2010 to 2016. $\begin{array}{cc} Years since & January 1, 2010 & Twitter user & (millions) \\ 0 & 30 & 3.5 & 232 \\ 0.5 & 49 & 4.0 & 255 \\ 1.0 & 68 & 4.5 & 284 \\ 1.5 & 101 & 5.0 & 302 \\ 2.0 & 138 & 5.5 & 307 \\ 2.5 & 167 & 6.0 & 310 \\ 3.0 & 204 & 6.5 & 317 \end{array}$

Use a calculator or computer to fit both an exponential function and a logistic function to these data. Graph the data points and both functions, and comment on the accuracy of the models.

sodni3 2021-02-09

Consider the following sequence. $s_{n} = 2 n - 1$
a) Find the first three terms of the sequence whose nth term is given.
$s_{1} =$
$s_{2} =$
$s_{3} =$
b) Classify the sequence as arithmetic, geometric, both, or neither. arithmetic geometric both neither If arithmetic, give d, if geometric, give r, if both, give d followed by r.

Efan Halliday 2021-02-09

What is Type of a DIfferential Equations?

Falak Kinney 2021-02-09

Use Gauss-Jordan row reduction to solve the given system of equations.
9x−10y =9
36x−40y=36

babeeb0oL 2021-02-09

Solve by factorization
$\frac{a}{a x - 1} + \frac{b}{b x - 1} = a + b$

Tammy Todd 2021-02-09

Rewrite without rational exponents, and simfly, if possible $256^{\frac{3}{4}}$

Jason Farmer 2021-02-08

Perform the modular arithmetic.
$(19 - 8) \mod 7$

CoormaBak9 2021-02-08

Suppose you purchase an iphoneX for $720 when it initially launched. The resale value decreases 3.08% each month since launch. Write an exponential function that models this situation, where t is the number of months after launch. Call it P(t). (round to the nearest thousandth.)

Mylo O'Moore 2021-02-08

State Cauchy-Riemann equations. Show that f(z) x*+ iy

Zoe Oneal 2021-02-08

Working with parametric equations Consider the following parametric equations.
a. Eliminate the parameter to obtain an equation in x and y.
b. Describe the curve and indicate the positive orientation.
$x = - 7 \cos 2 t, y = - 7 \sin 2 t, 0 \leq t \leq π$

Jaya Legge 2021-02-06

The exponential models the population of the indicated country, A, in millions, t years after 20006. Which country has the greatest growth rate? By what percentage is the population of that country increasing each year?
Country 1: $A = 26.3 e^{0.029 t}$
Country 2: $A = 127.7 e^{0.007 t}$
Country 3: $A = 148.5 e^{- 0.0091 t}$
Country 4: $A = 1094.2 e^{0.016 t}$

Jason Farmer 2021-02-06

First, construct the sixth degree Taylor polynomial $P_{6} (x)$ for function $f (x) = \sin (x^{2})$ about $x_{0} = 0$ The use $\int_{0}^{1} P_{6} (x) d x$ to approximate the integral $\int_{0}^{1} \sin (x^{2}) d x .$ Use 4-digit rounding arithmetic in all calculations. What is the approximate value?

defazajx 2021-02-06

Solve the following polynomial equation by factoring.
$9 x^{2} + 24 x + 16$

CoormaBak9 2021-02-06

A computer valued at $1500 loses 20% of its value each year. a. Write a function rule that models the value of the computer. b. Find the value of the computer after 3 yr. c. In how many years will the value of the computer be less than $500? Set your exponential function equal to $500 and solve or extend your table to determine the answer to part c.

djeljenike 2021-02-06

Consider that algebraic modeling For the function $f (x) = 34 {(1.024)}^{x}$
1) The function is an increasing exponential function because it is the form $y = a b^{x}$ and ?
2) The growth rate is ?
3) Thrawth factor is ?

Sinead Mcgee 2021-02-06

We need to calculate: the simplified form of $(3 \sqrt[3]{a^{3}} (- 5 \sqrt[4]{a^{3}}))$

coexpennan 2021-02-06

Simplify the expression and express the answer using rational exponents. Assume that all letters denote positive numbers. $\sqrt{x^{5}}$

Tazmin Horton 2021-02-06

The missing terms for the given polynomal p, q, r, and s such that
$q \neq 0 and s \neq 0, p q \cdot \frac{r}{s} = \frac{p r}{q s}$

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