Chapter 10: Problem 37
How much should be deposited in an account paying \(7.2 \%\) interest compounded monthly in order to have a balance of \(\$ 15,503.77\) three years from now?
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In Exercises, find the slope of the tangent line to the exponential function at the point \((0,1)\).
In Exercises, find the slope of the graph at the indicated point. Then write an equation of the tangent line to the graph of the function at the given point. $$ f(x)=\ln (x \sqrt{x+3}), \quad(1.2,0.9) $$
In Exercises, find the derivative of the function. $$ y=x^{2} e^{x}-2 x e^{x}+2 e^{x} $$
In Exercises, find the derivative of the function. $$ f(x)=x \ln e^{x^{2}} $$
In Exercises, use the given information to write an equation for \(y\). Confirm your result analytically by showing that the function satisfies the equation \(d y / d t=C y .\) Does the function represent exponential growth or exponential decay? $$ \frac{d y}{d t}=2 y, \quad y=10 \text { when } t=0 $$
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