Prove that for any natural n: athe number 7^(n+4) −7^n is divisible by 30.bthe number 3^(n + 2) −2^(n +2) +3^n −2^n is divisible by 10.

a) Let ; then , which is divisible by 30. We have

and since we know , it follows that for all .

b) We can write

and we're done.

the red lines denote the population of the bacteria after 35 hours. that would be 2,409.24. the y-intercept is the blue line which is 800 because that is the starting point. the equation used to make the graph is 800(1.032)^h, where h is the number of hours.

step-by-step explanation:

answer: it's upside down and i can't read it

step-by-step explanation: