# Solving Exponential Growth And Decay Problems

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.

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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.