A pattern of dots grows exponentially. The table shows the number of dots at each step of the pattern. Which equation represents the relationship between the step number, \( n , \) and the number of dots, \( y ?\)
A) \( y = n + 5 \)
B) \( y = 5 n \)
C) \( y = n ^ { 5 } \)
D) \( y = 5 ^ { n }\)
D
Find the solution of the exponential equation \( 16 e ^ { x } = 12 \) in terms of logarithms, or correct to four decimal places. \( x = \)
Certain radioactive material decays in such a way that the mass remaining after \( t \) years is given by the function
\( m ( t ) = 100 e ^ { - 0.01 t } \)
where \( m ( t ) \) is measured in grams. (a) Find the mass at time \( t = 0 \) . Your answer is (b) How much of the mass remains after \( 20 \) years? Your answer is Round answers to \( 1 \) decimal place.
