Math / Algebra

QuestionIf $y=(3 x+7)^{x}$ find $y(0)$ A. $\ln (7)$ B. 0 C. $\ln (7)+\frac{3}{7}$ D. $7 \ln (7)+3$ E. $7 \ln (7)-\frac{3}{7}$
Answer:

Studdy Solution

STEP 1

1. We are given the function $y = (3x + 7)^x$ .
2. We need to find the value of $y(0)$ .

STEP 2

1. Substitute $x = 0$ into the function.
2. Simplify the expression to find $y(0)$ .

STEP 3

Substitute $x = 0$ into the function $y = (3x + 7)^x$ :
$y(0) = (3(0) + 7)^0$

STEP 4

Simplify the expression:
$y(0) = (0 + 7)^0$ $y(0) = 7^0$

STEP 5

Recall the property of exponents that any non-zero number raised to the power of 0 is 1:
$7^0 = 1$
Therefore, $y(0) = 1$ .
The value of $y(0)$ is:
$\boxed{1}$
None of the provided options (A, B, C, D, E) match the result of $y(0) = 1$ . It seems there might be an error in the provided options.

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QuestionIf $y=(3 x+7)^{x}$ find $y(0)$ A. $\ln (7)$ B. 0 C. $\ln (7)+\frac{3}{7}$ D. $7 \ln (7)+3$ E. $7 \ln (7)-\frac{3}{7}$
Answer:

Studdy Solution

STEP 1

1. We are given the function $y = (3x + 7)^x$ .
2. We need to find the value of $y(0)$ .

STEP 2

1. Substitute $x = 0$ into the function.
2. Simplify the expression to find $y(0)$ .

STEP 3

Substitute $x = 0$ into the function $y = (3x + 7)^x$ :
$y(0) = (3(0) + 7)^0$

STEP 4

Simplify the expression:
$y(0) = (0 + 7)^0$ $y(0) = 7^0$

STEP 5

Recall the property of exponents that any non-zero number raised to the power of 0 is 1:
$7^0 = 1$
Therefore, $y(0) = 1$ .
The value of $y(0)$ is:
$\boxed{1}$
None of the provided options (A, B, C, D, E) match the result of $y(0) = 1$ . It seems there might be an error in the provided options.

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QuestionIf y=(3x+7)xy=(3 x+7)^{x}y=(3x+7)x find y(0)y(0)y(0) A. ln⁡(7)\ln (7)ln(7) B. 0 C. ln⁡(7)+37\ln (7)+\frac{3}{7}ln(7)+73​ D. 7ln⁡(7)+37 \ln (7)+37ln(7)+3 E. 7ln⁡(7)−377 \ln (7)-\frac{3}{7}7ln(7)−73​Answer:

Studdy Solution

STEP 1

1. We are given the function y=(3x+7)x y = (3x + 7)^x y=(3x+7)x.2. We need to find the value of y(0) y(0) y(0).

STEP 2

1. Substitute x=0 x = 0 x=0 into the function.2. Simplify the expression to find y(0) y(0) y(0).

STEP 3

Substitute x=0 x = 0 x=0 into the function y=(3x+7)x y = (3x + 7)^x y=(3x+7)x:y(0)=(3(0)+7)0 y(0) = (3(0) + 7)^0 y(0)=(3(0)+7)0

STEP 4

Simplify the expression:y(0)=(0+7)0 y(0) = (0 + 7)^0 y(0)=(0+7)0 y(0)=70 y(0) = 7^0 y(0)=70

STEP 5

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QuestionIf $y=(3 x+7)^{x}$ find $y(0)$ A. $\ln (7)$ B. 0 C. $\ln (7)+\frac{3}{7}$ D. $7 \ln (7)+3$ E. $7 \ln (7)-\frac{3}{7}$
Answer:

1. We are given the function $y = (3x + 7)^x$ .
2. We need to find the value of $y(0)$ .

1. Substitute $x = 0$ into the function.
2. Simplify the expression to find $y(0)$ .

Substitute $x = 0$ into the function $y = (3x + 7)^x$ :
$y(0) = (3(0) + 7)^0$

Simplify the expression:
$y(0) = (0 + 7)^0$ $y(0) = 7^0$