First differences are 2, 4, 8, 16, which is a geometric sequence. The parent function is not linear (constant first difference) or quadratic (first difference increases by the same amount from one to the next). When the first differences are a geometric sequence, the underlying sequence is a geometric (exponential) sequence.
1st blank: exponential
Translation up adds a constant to each of the f(x) values.
2nd blank: f(x)
3rd blank: increased by 5<span>
For the last blank, you're looking for an (x, f(x)) pair that is translated to (x, f(x)+5).
4th blank: </span><span>(2, 16)</span>
The answer is: " 5⁻ ⁵⁰ " .
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Note that: |7-9| = <span>| -2 | = 2 .
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Note: 5</span>³ * 5⁻⁵ = 5⁽ ⁽³⁾ ⁺ ⁽⁻⁵⁾ ⁾ = 5⁽³ ⁻ ⁵⁾ = 5⁻² ;
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Note: (5⁻⁹ * 5⁻² ÷ 5⁻¹³) = (5⁻⁹ * 5⁻²) ÷ 5⁻¹³ ;
→ (5⁻⁹ * 5⁻²) = 5⁽⁻⁹⁾ ⁺ ⁽⁻²⁾ = 5 ⁽⁻⁹ ⁻ ²⁾ = 5 ⁻¹¹ ;
→5 ⁻¹¹ ÷ 5⁻¹³ = 5 ⁽⁻¹¹⁾ ⁺ ⁽⁻¹³⁾ = 5⁽⁻¹¹ ⁻ ¹³⁾ = 5⁽⁻²⁴⁾
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→ [ 5⁽⁻²⁴⁾ ] ² = 5⁽⁻²⁴ * ²⁾ = 5⁽⁻⁴⁸⁾ ;
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Now, rewrite the entire problem; and solve:
→ 5⁽⁻⁴⁸⁾ * 5⁻² = 5⁽⁻⁴⁸⁾ ⁺ ⁽⁻²⁾ = 5⁽⁻⁴⁸⁻²⁾ ;
= 5⁻ ⁵⁰ .
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Answer:
I. 37+0.2m≤95
II. The greatest Distance you can drive each day is 290 miles.
Step-by-step explanation:
The cost of a car rental is $37 per day plus 20 cents per mile.
Let the number of miles driven be represented by m.
Therefore costs of miles driven
=20 cents X m =$0.2 X m= $0.2m
Total Cost Per day= Rental Cost + Cost of Miles Driven = 37+0.2m
Since the daily budget is $95, the total cost must be less than or equal to $95.
That is,
37+0.2m≤95.....(I)
This is the inequality that represents the greatest distance possible.
Next, we solve for m
37+0.2m≤95
0.2m≤95-37
0.2m≤58
m≤58/0.2
m≤290
The greatest Distance you can drive each day is 290 miles.