Question

Pls help me with this thank you!!

Answer 1

The ratios are approximately constant and equal to 0.7 which is indicative of an exponential relationship. The exponential equation is
`\(y = 50 * 0.7^x\)`.

To determine whether the relationship between x and y is linear or exponential, you can examine the ratio of consecutive y-values to see if it remains constant for a linear relationship or if it follows a constant multiplier for an exponential relationship.

Let's calculate the ratios for the given data:

`\[ (y_1)/(y_0) = (35)/(50) \approx 0.7 \]`

`\[ (y_2)/(y_1) = (24.5)/(35) \approx 0.7 \]`

`\[ (y_3)/(y_2) = (17.15)/(24.5) \approx 0.7 \]`

`\[ (y_4)/(y_3) = (12.005)/(17.15) \approx 0.7 \]`

`\[ (y_5)/(y_4) = (8.4035)/(12.005) \approx 0.7 \]`

`\[ (y_6)/(y_5) = (5.88245)/(8.4035) \approx 0.7 \]`

`\[ (y_7)/(y_6) = (4.117715)/(5.88245) \approx 0.7 \]`

The ratios are approximately constant and equal to 0.7. This suggests a consistent multiplier, which is indicative of an exponential relationship.

To find the exponential equation, you can write it in the form
`\(y = ab^x\)`, where a is the initial value and b is the constant multiplier.

Given the data, when x = 0, y = 50, so a = 50. The constant multiplier b is the ratio we found, which is approximately 0.7.

Therefore, the exponential equation is
`\(y = 50 * 0.7^x\)`.