154 results for "exponential".

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• Functions - Intersections
Needs to be tested
Question
Finding x and y intercapts and intersections of two graphs, one linear one exponential.
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• Log and exponential 1
Needs to be tested
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• Question in Calculus

A question to test basic differentiation of functions, including powers of x, trig, log and exponential functions.

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Differentiation by rule question with feedback given for anticipated student errors.
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Several graphs are drawn. Student should select those that are cubics

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Arrivals given by exponential distribution, parameter $\theta$ and $Y$, sample mean on inter-arrival times. Find and calculate unbiased estimator for $\theta$.

• 2012 2013 CBA3_3
Question

For a sample of size n from an Exponential distribution $\operatorname{Exponential}(\lambda)$  and given the mean of the sample, find the MLE for $\lambda$. Also find the expected information and a confidence interval for $\lambda$.

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Given the PDF for $Y \sim \operatorname{Exp}(\lambda)$ find the CDF, $P(a \le Y \le b)$ and $\operatorname{E}[Y],\;\operatorname{Var}(Y)$

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Calculating simple probabilities using the exponential distribution.

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Differentiate the function $(a + b x)^m e ^ {n x}$ using the product rule.

• Question

Differentiate $f(x)=x^{m}\sin(ax+b) e^{nx}$.

The answer is of the form:
$\displaystyle \frac{df}{dx}= x^{m-1}e^{nx}g(x)$ for a function $g(x)$.

Find $g(x)$.

• Question

Differentiate the following functions: $\displaystyle x ^ n \sinh(ax + b),\;\tanh(cx+d),\;\ln(\cosh(px+q))$

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The derivative of $\displaystyle \frac{a+be^{cx}}{b+ae^{cx}}$ is $\displaystyle \frac{pe^{cx}} {(b+ae^{cx})^2}$. Find $p$.

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Differentiate $\displaystyle e^{ax^{m} +bx^2+c}$

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Question on the exponential distribution involving a time intervals and arrivals application, finding expectation and variance. Also finding the probability that a time interval between arrivals is less than a given period. All parameters and times randomised.

• Powers and indices
Exam (7 questions)

Questions on powers, the laws of indices, and exponential growth.

• Exponential increase
Question

Work out the average percentage increase per year in price of an item, given two prices several years apart.

• Exam (40 questions)
Students will assess their ability to solve  problems involving logs and exponentials.
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• Exam (40 questions)
Students will review and practice problems involving logs and exponentials.
• Exam (16 questions)
Students will find the inverse of log and exponential functions.
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