Question The graph $y=500(0.85)^{x}$ represents the amount of drug (in mg) left in a patient's system $x$ hours after administration. Find the $y$ -intercept.

Studdy Solution

STEP 1

1. The equation $y=500(0.85)^{x}$ is an exponential function representing the decay of a drug in a patient's system over time.
2. The $y$ -intercept of a graph is the point where the graph crosses the $y$ -axis, which occurs when $x=0$ .

STEP 2

1. Determine the $y$ -intercept by evaluating the function at $x=0$ .

STEP 3

Evaluate the function $y=500(0.85)^{x}$ at $x=0$ to find the $y$ -intercept.
$y = 500(0.85)^0$

STEP 4

Recall that any nonzero number raised to the power of 0 is 1.
$(0.85)^0 = 1$

STEP 5

Substitute $(0.85)^0 = 1$ into the function to find the value of $y$ .
$y = 500 \cdot 1$

STEP 6

Calculate the product to find the $y$ -intercept.
$y = 500$
The $y$ -intercept of the graph is the point $(0, 500)$ .

Was this helpful?

Question The graph $y=500(0.85)^{x}$ represents the amount of drug (in mg) left in a patient's system $x$ hours after administration. Find the $y$ -intercept.

Studdy Solution

STEP 1

1. The equation $y=500(0.85)^{x}$ is an exponential function representing the decay of a drug in a patient's system over time.
2. The $y$ -intercept of a graph is the point where the graph crosses the $y$ -axis, which occurs when $x=0$ .

STEP 2

1. Determine the $y$ -intercept by evaluating the function at $x=0$ .

STEP 3

Evaluate the function $y=500(0.85)^{x}$ at $x=0$ to find the $y$ -intercept.
$y = 500(0.85)^0$

STEP 4

Recall that any nonzero number raised to the power of 0 is 1.
$(0.85)^0 = 1$

STEP 5

Substitute $(0.85)^0 = 1$ into the function to find the value of $y$ .
$y = 500 \cdot 1$

STEP 6

Calculate the product to find the $y$ -intercept.
$y = 500$
The $y$ -intercept of the graph is the point $(0, 500)$ .

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Question The graph y=500(0.85)xy=500(0.85)^{x}y=500(0.85)x represents the amount of drug (in mg) left in a patient's system xxx hours after administration. Find the yyy-intercept.

Studdy Solution

STEP 1

1. The equation y=500(0.85)xy=500(0.85)^{x}y=500(0.85)x is an exponential function representing the decay of a drug in a patient's system over time.2. The yyy-intercept of a graph is the point where the graph crosses the yyy-axis, which occurs when x=0x=0x=0.

STEP 2

1. Determine the yyy-intercept by evaluating the function at x=0x=0x=0.

STEP 3

Evaluate the function y=500(0.85)xy=500(0.85)^{x}y=500(0.85)x at x=0x=0x=0 to find the yyy-intercept.y=500(0.85)0 y = 500(0.85)^0 y=500(0.85)0

STEP 4

Recall that any nonzero number raised to the power of 0 is 1.(0.85)0=1 (0.85)^0 = 1 (0.85)0=1

STEP 5

Substitute (0.85)0=1(0.85)^0 = 1(0.85)0=1 into the function to find the value of yyy.y=500⋅1 y = 500 \cdot 1 y=500⋅1

STEP 6

Calculate the product to find the yyy-intercept.y=500 y = 500 y=500The yyy-intercept of the graph is the point (0,500)(0, 500)(0,500).

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Question The graph $y=500(0.85)^{x}$ represents the amount of drug (in mg) left in a patient's system $x$ hours after administration. Find the $y$ -intercept.

1. The equation $y=500(0.85)^{x}$ is an exponential function representing the decay of a drug in a patient's system over time.
2. The $y$ -intercept of a graph is the point where the graph crosses the $y$ -axis, which occurs when $x=0$ .

1. Determine the $y$ -intercept by evaluating the function at $x=0$ .

Evaluate the function $y=500(0.85)^{x}$ at $x=0$ to find the $y$ -intercept.
$y = 500(0.85)^0$

Recall that any nonzero number raised to the power of 0 is 1.
$(0.85)^0 = 1$

Substitute $(0.85)^0 = 1$ into the function to find the value of $y$ .
$y = 500 \cdot 1$

Calculate the product to find the $y$ -intercept.
$y = 500$
The $y$ -intercept of the graph is the point $(0, 500)$ .