7. Since the temperature is being increased by +0.25 every hour, this will be an arithmetic sequence, so it can be solved using the arithmetic sequence formula. The formula is [tex]a_n = a_1 + (n - 1)d[/tex], where [tex]a_1[/tex] is the first term of the sequence (4.5), d is the common difference (0.25), and n is the number of the term you want to find. Since you already have the value of the term you want to find, you can put that where [tex]a_n[/tex] is and solve for n.
[tex]a_n = a_1 + (n - 1)d[/tex] Plug in what you know
22.25 = 4.5 + (n - 1)(0.25) Subtract 4.5 from both sides
17.75 = (n-1)(0.25) Divide both sides by 0.25
71 = n - 1 Add 1 to both sides
72 = n Switch the sides to make it easier to read
n = 72
So, the temperature of the liquid will reach 22.25°C in hour 72.
8. The formula used in this problem is f(t) = f_{1} * r^{t-1}, where r is the common ratio. The common ratio is how you get from one term to the next. In this case, the common ratio is ·4, so from one year, or term, to the next the number of frogs is multiplied by four. This makes the answer B. The number of frogs quadruples every year.
