To determine when the coin will be worth $150, you can substitute 150 for y and solve for t. What value do you get for t when you do that?

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.