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A collection of resources to provide ideas for setting exponential growth and decay in the context of engineering, together with materials to support teaching of these topics.
The main focus is on solving problems involving exponential growth and decay. 'Exponential graphs' is a 'Core Maths' resource that asks students to match graphs into different classes.
'Logarithms' is a RISP 'always, sometimes or never true' activity where students need to be familiar with logs in different number bases.
This resource could be used as a prelude to the ' Power Demand' activity.
requires students to form equations given a set of cards and to determine, with examples, whether the equation is always, sometimes or never true and to attempt to say why.
Such a relation between an unknown function and its derivative (or derivatives) is what is called a differential equation.
Solving Exponential Growth And Decay Problems Salvation Langston Hughes Essay Summary
Many basic ‘physical principles’ can be written in such terms, using ‘time’ $t$ as the independent variable.
But it's still not so hard to solve for $c,k$: dividing the first equation by the second and using properties of the exponential function, the $c$ on the right side cancels, and we get $$=e^$$ Taking a logarithm (base $e$, of course) we get $$\ln y_1-\ln y_2=k(t_1-t_2)$$ Dividing by $t_1-t_2$, this is $$k=$$ Substituting back in order to find $c$, we first have $$y_1=ce^$$ Taking the logarithm, we have $$\ln y_1=\ln c t_1$$ Rearranging, this is $$\ln c=\ln y_1-t_1= $$ Therefore, in summary, the two equations $$y_1=ce^$$ $$y_2=ce^$$ allow us to solve for $c,k$, giving $$k=$$ $$c=e^$$ A person might manage to remember such formulas, or it might be wiser to remember the way of deriving them.
A herd of llamas has 00$ llamas in it, and the population is growing exponentially. Write a formula for the number of llamas at arbitrary time $t$.
Mathematics This engineering resource asks the question: how can you predict future power requirements?
Students are required to complete a table by substituting values into a formula and plot a graph.