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For questions 295 to 299, solve, rounding to two decimal places when needed.
Refer to the following inverse properties, as needed.
295. 8log2(3x – 1) = 256
296. ln 8x = 3.5
297. 4000(1.005)
x = 12,000
298. 75e
0.05x = 150
299. e
6x 1 = e
4x–4
300. Radioactive elements undergo radioactive decay. The amount remaining, A,
of a radioactive substance after t years is given by , where A0
is
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the initial amount of radioactive substance and k is its half-life. How much
of a 20-gram sample of carbon- 14, which has a half-life of 5730 years,
remains after 5000 years?
301. The formula for the pH of an aqueous solution is given by f(x) = – log10 x,
where x is the hydronium ion concentration (in moles per liter) of the
solution. Find the pH of diet soda Z, which has a hydronium concentration
of 7.6 × 10
–4
.
302. The compound interest formula is P = P0 (1 r)
t
, where r is the rate,
compounded annually, and P is the value after t years of an initial
investment of P0
. Suppose that the grandparents of a newborn child
establish a trust fund account for the child with an investment of $50,000.
Assuming no withdrawals and no additional deposits are made,
approximately what interest rate compounded annually is needed to double
the investment in 20 years?
Other Common Functions
303. Suppose . Find each of the indicated function values.
(A) f(–1)
(B)
(C) f(0)
(D) f(5.5)
(E) f(3)
304. Suppose f(x) = [x], the greatest integer function. Find each of the following
function values.
(A) f(3.99)
(B) f(–3.99)
(C) f(0.005)
(D) f(–15)
(E) f(π)
For questions 305 to 309, find the solution set. Refer to the following properties
of the absolute value function, as needed.
|x| ≥ 0
|xy| = |–x|
|xy| = |x||y|
|u v| ≤ |u| |v|
|x| = 0 if and only if x = 0
If c > 0, then
|x| = c if and only if either x = c or x = –c
|x| < c if and only if –c < x c if and only if either x c
Note: Properties involving hold if you replace with ≥.
305.
306. |–2x – 3| < 15
307. |5x| ≥ 40
308. –2|4x 1| ≥ –10
309. |x| < –1
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For questions 310 to 312, evaluate the power function f defined as f(x) = x
a
,
where a is a real number. Round to two places, when needed.
310. f(x) = x
–3
; f(10)
311. f(x) = x
0.75
; f(256)
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