Write an exponential function in the form y=ab^x that goes through points (0,7) and (5,1701).

Mathematics

1 answer:

Marizza181 [45]3 years ago

3 0

Answer:

y = 7 $3^{x}$

Step-by-step explanation:

Use the given ordered pairs to find a and b

Using (0, 7 ), then

7 = a $b^{0}$ ( $b^{0}$ = 1 ), thus

a = 7

y = 7 $b^{x}$

Using (5, 1701 )

1701 = 7 $b^{5}$ ( divide both sides by 7 )

243 = $b^{5}$ ( take the fifth root of both sides )

b = $\sqrt[5]{243}$ = 3 , thus

y = 7 $3^{x}$

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joe weighs 20lbs.less yhantwice jeffs weight.if jeff would gain 10lbs.,then together they wouldweigh 250lbs. how much does each

masya89 [10]

So,

Let x represent Joe's weight and y represent Jeff's weight.

"Joe weighs 20 lbs. less than twice Jeff's weight."
x = 2y - 20

"If Jeff would gain 10 lbs., then together they would weigh 250 lbs."
(y + 10) + x = 250

We now have our two open sentences.
x = 2y - 20
(y + 10) + x = 250

Get rid of parentheses.
x = 2y - 20
x + y + 10 = 250

We will use Elimination by Substitution.
2y - 20 + y + 10 = 250

Collect Like Terms.
3y - 10 = 250

Add 10 to both sides.
3y = 260

Divide both sides by 3.
$Jeff's\ weight = 86 \frac{2}{3} \ lbs.$

Substitute again.
$x = 2(86 \frac{2}{3} )-20$

Multiply.
$x = 173 \frac{1}{3} -20$

Subtract.
$Joe's\ weight = 153 \frac{1}{3}\ lbs.$

Check.

"Joe weighs 20 lbs. less than twice Jeff's weight."
Jeff's weight times two is 173 and one-third.
20 lbs. less than that is 153 and one-third lbs. Check.

"If Jeff would gain 10 lbs., then together they would weigh 250 lbs."
86 and two-thirds + 10 = 96 and two-thirds.
96 and two-thirds + 153 and one-third equals 250 lbs. Check.

$Joe's\ weight\ is\ 153 \frac{1}{3} \ lbs.$
$Jeff's\ weight\ is\ 86 \frac{2}{3} \ lbs.$

3 0

3 years ago

5=1/3(2x+12)<br><br> Solve for X in simplest form

garik1379 [7]

9514 1404 393

Answer:

x = 3/2

Step-by-step explanation:

Multiply by 3 and solve the resulting 2-step equation.

5 = (1/3)(2x +12)

15 = 2x +12 . . . . . . multiply by 3

3 = 2x . . . . . . . . . . subtract 12