Answer:
Difference: 32
Step-by-step explanation:
To provide an integer estimate for [tex]5^\pi[/tex], we can first approximate the value of [tex]\pi[/tex]. A common approximation for [tex]\pi[/tex] is 3.14. Thus, we'll use this approximation to estimate [tex]5^\pi[/tex].
[tex]5^{3.14}[/tex]
Since it very hard to evaluate [tex]5^{3.14}[/tex], so, we can round 3.14 as 3 in nearest whole number.
[tex] 5^{3} = 125[/tex]
Now, let's find [tex]5^\pi[/tex] on a calculator:
[tex]5^\pi = 156.9925453 [/tex]
The difference between the estimate [tex]125[/tex] and the calculator value [tex]184.52[/tex] is:
[tex] 156.9925453 - 125 \approx 31.99254531 \approx 32 [/tex]
So, the difference between the estimated value and the calculator value is approximately [tex]32[/tex].
