Question

A hiker on the Appalachian Trail planned to increase the distance covered by 10% each day. After 7 days, the total distance traveled is 75.897 miles.If this pattern continues, what is the total number of miles the hiker will travel in 10 days? Round your answer to the hundredths place

Answer 1

Step 1:

Use the exponential increase formula

$\begin{gathered} A=P(1+r)^n \\ A\text{ = total number of miles travel in 10 days} \\ \text{P = Initial value} \\ r\text{ = rate in \%} \\ n\text{ = time in days} \end{gathered}$

Step 2:

r = 10% = 0.1

P = 75.897

n = 3 days

Step 3:

$\begin{gathered} A\text{ = 75.897 }\times(1+0.1)^3 \\ A\text{ = }75.897\text{ }\times(1.1)^3\text{ } \\ A\text{ = }75.897\text{ }\times\text{ 1}.331 \\ A\text{ = 101.02 miles} \end{gathered}$

Final answer

Final answer

101.02 miles