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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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Answer:

Step-by-step explanation:

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Look the formula up online to find out what each variable represents if needed.

We are solving for P, which is the principal amount 5 years back.

Substitute 11,000 for A (total amount), 4.5% for r(rate), 2 for n(number of times -- in this case, semiannually), and 5 for t(time -- 5 years).

11000 = P[1+(0.045/2)]^(2x5)

11000 = P (1.0225)^10

11000 = P (1.2492)   approx.

Divide both sides by 1.2492 to find P.

P = $8805.64  (approx)

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