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3 years ago

Find the exponential equation for the given information. Pls help

Mathematics

1 answer:

nikitadnepr [17]3 years ago

3 0

Answer:

y = 12 $(2.9)^{x}$

Step-by-step explanation:

The standard form of the exponential function is

y = a $(b)^{x}$

Find a and b by substituting ordered pairs from the table into the equation

Using (0, 12 ), then

12 = a $b^{0}$ ( $b^{0}$ = 1 ), so

a = 12, then

y = 12 $b^{x}$

Using (1, 34.8 ) , then

34.8 = 12 $b^{1}$ ( divide both sides by 12 )

b = 2.9

Thus exponential function is

y = 12 $(2.9)^{x}$

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The explicit rule for a sequence is an=5(−2)^n−1

Murrr4er [49]

Answer:

3) $a_n=-2a_{n-1}$ , $a_1=5$

Step-by-step explanation:

Given that the explicit rule for a sequence is $a_n=5(-2)^{n-1}$ .

Now we need to find about what is the recursive rule for the sequence and match with the given choices to find the correct choice.

1) $a_n=-2a_{n+1}$ , $a_1=5$

2) $a_n=-5a_{n+1}$ , $a_1=2$

3) $a_n=-2a_{n-1}$ , $a_1=5$

4) $a_n=-5a_{n-1}$ , $a_1=2$

Plug n=1 into given formula to get first term

$a_n=5(-2)^{n-1}$

$a_1=5(-2)^{1-1}=5(-2)^{0}=5(1)=5$

base of the exponent part is (-2) so that means we need to multiply -2 to the previous term to get nth term

Hence correct choice is: 3) $a_n=-2a_{n-1}$ , $a_1=5$

7 0

3 years ago

Please help I found this one a bit confusing

Brums [2.3K]

Answer:

7.2

Step-by-step explanation:

To reach point D from point C, you need to add 4 to the x-value of point C and take away 6 from the y-value. These numbers are the sides of the hypothetical triangle.

The Pythagorean Theorem states that $a^2+b^2=c^2$ . If we plug the side lengths in for a and b, we get $4^2 + 6^2 = c^2$ . This can be simplified to $16+36=c^2$ , or $52 = c^2$ . If we root both sides, we find that c is equal to $\sqrt{52}$ , which is slightly more than 7, at around 7.2.