Answer:
5.23 years, the time at which the coin has increased in value to $150.
Step-by-step explanation:
Use the exponential function f(t) = 4*2^t.
Substitute $150 for f(t): $150 = 4*2^t.
Simplify this by dividing both sides by 4: $150/4 = 2^t, or $37.50 = 2^t.
Next, solve for the value of t. To do this, take the common log of both sides, obtaining:
log 37.50 = t*log 2. Thus, t = [log 37.50] / [log 2]. Evaluate this using a calculator:
t = 1.57403 / 0.30103 = 5.23 time units. For example, this could be 5.23 years.
