Esh deposits $3500 in an account that earns 3.75% interest each year. After the
first year, Esh has $3631.25 in the account.
After the second year, Esh has $3767.42 in
the account, and after the third year Esh has
$3908.70 in the account.

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Ответ:

gamerdoesart

02.04.2020

Mathematics

$y=\displaystyle\int_0^x\frac2{1+3t+t^2}\,\mathrm dt$

By the fundamental theorem of calculus,

$\dfrac{\mathrm dy}{\mathrm dt}=\dfrac2{1+3x+x^2}$

then by standard differentiation,

$\dfrac{\mathrm d^2y}{\mathrm dt^2}=-\dfrac{6+4x}{(1+3x+x^2)^2}$

is concave upward whenever $\dfrac{\mathrm d^2y}{\mathrm dt^2}0$ . The denominator is always positive, so the sign is determined by the numerator alone:

$6+4x0\implies x-\dfrac32$

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Esh deposits $3500 in an account that earns 3.75% interest each year. After the first year, Esh has $3631.25 in the account. After the second year, Esh has $3767.42 in the account, and after the third year Esh has $3908.70 in the account.