Find a formula for the exponential function of the form A=f(t)=IB^t passing through the points (2.5, 17) and (7.4, 4) A = f(t) =?

Q: Suppose 15 blackberry plants started growing in a yard. Absent constraint, the blackberry plants…

A: Please refer the attached image for complete solution.

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Q: Solve th equation for x. log2(log3 x) = 4

A: Consider the given: log2log3x=4Using log Rule:logap=n is equivalent to p=an,log2log3x=4…

Q: What exponential function will pass through both (0,6) and (1,3)?

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Q: Find the present value of $4000 payable at the end of 4 years, if money may be invested at 6% with…

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Q: Suppose the population of a certain bacteria in a laboratory sample is 100. If it doubles in…

A: The initial population of the bacteria is, P0=100. After every t=6, the population doubles. So, the…

Q: To get $800 after 212years at 8% compounded continuously

A: $800 after 212 years at 8% compounded continuously.

Q: The rate of a continuous money flow starts at $1000 and increases exponentially at 5% per year for 4…

A: We use the formula                                P = ∫0T f(t)e-rt dt

Q: The half-life of carbon-14 is 5700 years. If an item is discovered with only 17% of the original…

A: Given Half life of carbon-14 =5700 years  i.e. and an item is found with only 17% of the original…

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Q: A population of 200 kangaroo is released into the forest. During the first three years, the…

A: Given,initial kangaroo number, n(0) = 200number of kangaroo after 3 years, n(3) =500carrying…

Q: A colony of bacteria is grown under ideal conditions in a laboratory so that the population…

A: Consider the following exponential function: y=abx                                  ...... 1 Here,…

Q: Express in terms of sums and differences of logarithms. 2 In In 3 3x y 2 3 3x y

A: Given:ln23x3ywe need to express this logarithm in terms of sums and differences.We know thatln (ab)…

Q: 1) loga(3-1ogalx-)=2

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Q: The accumulated amount of P8000 is P10000 after 2 years, calculate the interest rate if it is…

A: The accumulated amount of $8000 is $10000 after 2 years,   We have to calculate the interest rate…

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Q: The mass reaches 75 grams after t= years.

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Q: Find a formula for the exponential function passing through the points (-2, - -) and (1,20) 16

A: -2,516 and 1,20 Let the exponential function be yn=abxn. Substitute both the point in the assumed…

Q: If there are 520 grams of Tadioactive material with a half-life of 12 hours, how TIuch of the…

A: The material is decaying at a constant rate, every 12 hours it is getting halved.  So, it is an…

Q: Find a formula for the exponential function passing through the points (-3,- -) and (2,32) 32 y =

A: The standard form of exponential function is given below: y=abx where, a≠0, b>0 and b≠1.

Q: $400 invested at 7% compounded continuously after aperiod of 3 years

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Q: $5,000 is invested in an account earning 6% interest (APR), compounded continuously. How much is in…

A: Total investment P=$5000 Rate of interest R= 6% Time t=3 years Total amount after 3 years

Q: The rate of a continuous money flow starts at ​$600 and increases exponentially at 4% per year for…

A: Given, Initial amount P0 = $600 R = 4% = 0.04 T = 15 years

Q: Find the time needed to double an investment at 8% annual interest rate compounded continuously.

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Q: solve for y: ln(3-y)-ln(y) = 2x + ln(5) without a calculator

A: Given equation is :Moving all the logarithm terms and using the property: ln(a) – ln(b) =…

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Q: Suppose a study is completed that finds that the number of cockroaches in Chandler decreases by 18%…

A: Given the number of cockroaches decrease by 18% every 12 years. We first find an equation using the…

Q: An investment earns 5.1% yearly interest compounded continuously and is currently growing at the…

A: Solution:Given    i=5.1%     n=1     A=765   To find P=?Formula:A=P(1+i)n

Q: A quantity with an initial value of 8200 grows continuously at a rate of o.55% per decade. What is…

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Q: Suppose that the number of bacteria in a certain population increases according to a continuous…

A: Topic-basic maths

Q: Determine how long it will take for an initial investment to double if it earns 7% interest per year…

A: The time take to double the initial investment is approximately 10 years  see the calculation below

Q: Jose invests $10,000 at 10% interest that is compounded continuously. Which is the value after 10…

A: We have to find compound amount

Q: The number of bacteria in a certain population increases according to a continuous exponential…

A: Here we will find the number of hours  for sample to double its size,

Q: Find the effective rate of interest for 10% compound continuously.

A: The continuous rate is calculated by raising the number "e" (approximately equal to 2.71828) to the…

Q: What are the blanks?

A: Note: We are authorized to answer three sub-parts at a time. Since you have asked more than three…

Q: When do we use the Chain rule in derivates of exponential function

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Q: express ln 3√4 in terms of ln 2 and/or ln 3

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Q: Find a formula for the exponential function passing through the points (-2, -) and (1, 6). 3 y%3D

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Q: A freshly inoculated bacterial culture of Streptococcus contains 100 cells. When the culture is…

A: General expression for exponential growth function is given by,                   n(t) = a(1+r)t…

Q: A quantity with an initial value of 8200 grows continuously at a rate of 0.55% per decade. What is…

A: Initial Value=  8200. Growth rate= 0.55% . We can formulate the following equation for "t" years :…

Q: Give 5 example of integrals yielding natural log functions with solution

A: The integral examples are:

Q: Find the total accumulated amoun

A: Given: Invested amount = $6500 Interest rate = 5 %

Q: Find the present value of $1000 payable at the end of 3 years, if money may be invested at 8% with…

A: This is a question based on compound interest. we have to calculate on the basis of continuous…

Q: Find a formula for the exponential function passing through the points (-2,- -) and (1,20) 25

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Q: A quantity with an initial value of 3600 grows continuously at a rate of 2.5% per decade. What is…

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Q: A sample of bacteria taken from a river has an initial concentrationof 2.5million bacteria per…

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Q: When we take measurements of the same general type, a power law of the form y = ax often gives an…

A: (b)   Given that X´=log(X) and Y´=log(Y)   X Y X´ Y´ 2 1.81 0.30103 0.257679…

Q: At the beginning of the COVID-19 pandemic, the number of new cases was growing exponentially. There…

A: Here, the exponential model is given by: P(t)=a×bt...(1) where P(t) is the number of cases after a…

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!