Radioactive Decay The amount of radioactiveisotope thorium-234 present at time t is given byA(t) = 500e-0.02828tgrams, where t is the time inyears that the isotope decays. The initial amountpresent is 500 grams.a. How many grams remain after 10 years?b. Graph this function for 0 <= t <= 100.c. If the half-life is the time it takes for half of theinitial amount to decay, use graphical methods toestimate the half-life of this isotope.

Q: decreasing. is increasing log x or Find the intervals in whichf(x)D

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Q: Calculate. 4+21080.4 5) (log²8- log²125)(logo.44

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Q: Find the domain of the function. f(x) = log (x+ 10) %3D O A. (- 10,00) Ов. O B. (1,00) c. O C.…

A: Domain is the possible values of x.Inside logarithm we should have positive numbers only.

Q: 3) Find the formula for an exponential function y = ab* that passes thru the two points. Round 6 to…

A: Given,  An exponential function  y = abx  It passes through the points  a  0, 6, 3, 750 b 1, 6, 5, 1…

Q: Create an approximate exponential model for the data set. 1. 1 2 -2 4. f(x) 1.2 1.6 2.0 2.6 3.4 f(x)…

A: To find f(x) using 1 as reference.

Q: 3. Solve. Show steps. 2 log x' - 5log x = 3

A:

Q: Brand A light bulbs have exponential life times, with mean 1 year. Brand B light bulbs have…

A: We have given that Brand A light bulbs have exponential life times, with a mean of year. and Brand…

Q: The length of a stalactite (in mm) has been measured at the beginning of every fourth year since the…

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Q: Evaluation Construct the table and draw the graph of the functions y = (2/5)* and y = log{2/5) ×

A: Given: y=25x y=log2/5x

Q: = (5+ cx*)** y=(5+6x*) (tan(7x)° 312 hint log.differentiat use %3D

A: logab=bloga ddxtan2ax=a sec2 ax

Q: Solve for x in log,(x+ 1) + log, (x – 1) = log, 15. A. X = 5 В. Х 3 4 C. x +4 D. X = 3 or x= 1…

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Q: Red Blue Black Green + Match each equation with a graph above v 10* a. blue v log(z) b. red et C.…

A: Given: To find: Match the graph with the colours.

Q: Column B Column A a. 1 1. log3(1/9) b. -2 2. log5 C. 3. logs25 d. 2 log1o(1/1000) 4. -3 e. 5. log41

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Q: The impaet G Inflation on a K20,000 pension 'can measured by the purchasing power kro,000 apde, t…

A: P=20000e-0.0495t Differentiating with respect to t, we get…

Q: The graph shown represents population growth. Time (years) A. exponential (J-curve) B. negative D.…

A: Exponential growth occurs when the resources are sufficiently enough and logistic growth occurs when…

Q: 1. Rewrite each logarithmic expression as an exponential expression. a. log4(2x) = 3 b. log 1= 0 c.…

A: We need to write log expression into exponential expression.

Q: . The population of a town reaches 113000. 7 years ago the population was 82000. Assuming that the…

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Q: Solve the equation for : 62 3

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.