Question

for the last fifteen years, the price of gold has increased dramatically. in 2003 the average price for an ounce of gold was $270.since 2003, its value can be modeled as a function to the following exponential equation, P= 270(2)^t/4where p = the average price of an ounce of gold and t= the time since 2001 in years. Write this exponential equation in an equivalent logarithmic format in order to solve for t.

Answer 1

Assuming the exponent of (2) in the equation is (t/4):

P = 270 * 2^(t/4)

P/270 = 2^(t/4)

log2 (P/270) = log2 (2^(t/4))

log2 (P/270) = t/4

t = 4*log2 (P/270)

Now, assuming t is the exponent of (2), we have:

P = 270 * (2^t)/4

4P/270 = 2^t

log2 (4P/270) = log2 (2^t)

log2 (4P/270) = t

t = log2 (4) + log2 (P/270) = 2 + log2 (P/270)