Question Estimate the solution, to the nearest tenth, for the equation $-2x+9=5^x$ using the provided table.

Studdy Solution

STEP 1

Assumptions
1. The given equation is $-2x+9=5^x$
2. The values in the table are approximations rounded to the nearest tenth
3. We are looking for a solution to the equation where the values of $-2x+9$ and $5^x$ are approximately equal

STEP 2

First, we need to examine the table and find the row where the values of $-2x+9$ and $5^x$ are closest to each other.

STEP 3

Looking at the table, we can see that the values of $-2x+9$ and $5^x$ are closest to each other when $x=1.15$ . At this point, $-2x+9$ is approximately 6.7 and $5^x$ is approximately 6.4.

STEP 4

Given that the values in the table have been rounded to the nearest tenth, we can conclude that $x=1.15$ is a solution to the equation $-2x+9=5^x$ to the nearest tenth.
So, $x \approx 1.15$

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