Answer:
[tex]A_{1}=57^{0}F; A_{4}=70^{0}F; A_{6}=80^{0}F; r=1.07[/tex]
Step-by-step explanation:
The formula for calculating the nth term of a Geometric Sequence is given as: [tex]A_{n}=ar^{n-1}[/tex] where n is the number of term, r=common ratio and a=first term.
At hour 4, the temperature is [tex]70^{0}[/tex]F
[tex]A_{4}=70, n=4\\70=ar^{4-1}=ar^{3}[/tex].......(i)
At hour 6 the temperature is 80°F.
[tex]A_{6}=80, n=6\\80=ar^{6-1}=ar^{5}[/tex]......(ii)
Solving (i) and (ii) simultaneously
[tex]\frac{80}{70}=\frac{ar^{5}}{ar^{3}} \\x^{2} r^{2} =\frac{8}{7}\\r=\sqrt{\frac{8}{7}}=1.07[/tex]
Plugging r into equation (i), we could use (ii) as well,
[tex]70=ar^{3}[/tex]
[tex]70=a(\sqrt{\frac{8}{7}})^{3}[/tex]
[tex]a=\frac{70}{\sqrt{(\frac{8}{7}})^{3}}[/tex]
[tex]a=\frac{245}{8}\sqrt{\frac{7}{2} }[/tex] =57.29
Therefore:
[tex]A_{1}=57^{0}F; A_{4}=70^{0}F; A_{6}=80^{0}F; r=1.07[/tex]
Answer:
The other user gave an amazing explanation but their final answer is a bit confusing, so to sum it up, here's the answer: 57(1.07)
Have a wonderful day!
Step-by-step explanation:
