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

Solve equations involving logs and exponential functions, by using inverse operations.

Calculating the amount of money in a savings account after a given amount of time, and calculating how long it will take for the amount of savings to exceed a given value. 

The easiest type of exponential to graph where the base is greater than 1 and no transformations take place.

Calculating the derivative of an exponential function of the form $ae^{bx}$, using a table of derivatives.

Multiple choice question. Given a randomised polynomial select the possibe ways of writing the domain of the function.

Graphing $y=ab^{\pm x+d}+c$

Graphing $y=ab^x+c$

Graphing exponentials with a base between 0 and 1 and no transformations take place.

The easiest type of exponential to graph where the base is greater than 1 and no transformations take place.

The easiest type of exponential to graph where the base is greater than 1 and no transformations take place.

Using basic derivatives to calculate the gradient function of a hill $y=-e^x+b\ln\left(x\right)+c$, and then substituting values to find the gradient at specific distance from the sea. 

Differentiating further exponentials

Differentiating exponentials

Differentiating further exponentials

Differentiating further exponentials

Differentiating exponentials

Differentiating further exponentials

Knowing the doubling time of a population and the population on day $t$, calculate the initial population and the number of days required for the population to reach a threshold. 

This question gives the student the formula for the charge on a capacitor as a function of time then asks them to find the value of k, the exponential constant given other values and hence write out the formula for the given case. A custom function (in Extensions & scripts) extracts the student's formula and plots it on a JSXGraph object in the question. The student is then asked to evaluate the function at a given point using the plot or other methods. The value of the capacitor (Q_0), time (t) and charge at time t are randomised as is the value at which the formula is to be evaluated.

Calculating the rate of change of the temperature during a chemical reaction using the chain rule in a function of the form $T=ate^{-t}$, and finding the maximum temperature of the reaction.

Knowing the half-life of Carbon-14 and the initial mass of Carbon-14 when a tree was cut (a) write an expression that describes the relationship between the remaining mass and time, (b) calculate the remaining mass after $t$ years, and (c) given the remaining mass calculate how many years ago the tree was cut down. 

The expected answer involves the logarithm of a negative number, which doesn't have a unique solution.

The part's marking algorithm evaluates the exponential of the student's answer and the expected answer, and compares those.

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

Differentiating exponentials and Logs

Questions testing rather basic understanding of the index laws.

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