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nikklg [1K]
3 years ago
5

The value of an autographed baseball from 2017 is $300. The value of the baseball exponentially increases by 5% each year after

2017. Write a one-variable inequality that could be used to solve for the number of years, x, it would take for the baseball to be worth at least $650.
Do not use any dollar signs in the inequality. Write the inequality in standard form.
Mathematics
1 answer:
WARRIOR [948]3 years ago
7 0
General exponential equation
y = A(1+r)^x
where
A = initial value
r = rate increase (+) or decrease (-)
x = time period of the change
y = projected value

y = 300(1.05)^x
in this problem, x = years after 2017
we want to find an x that makes the value more than or equal to 650

650 <= 300(1.05)^x
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Given

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T(e_1) = (1,2)

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T(e_1) = (1,2) = \left[\begin{array}{c}1\\2\end{array}\right]

T(e_2) = (-4,6)=\left[\begin{array}{c}-4\\6\end{array}\right]

T(e_3) = (2,-6)=\left[\begin{array}{c}2\\-6\end{array}\right]

Substitute the above expressions in A = [T(e_1)\ T(e_2)\ T(e_3)]

A = \left[\begin{array}{ccc}1&-4&2\\2&6&-6\end{array}\right]

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A = \left[\begin{array}{ccc}1&-4&2\\2&6&-6\end{array}\right]

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