if z(t) = 60 * 1.03^t, find t when z(t) =144

144/60 = 1.03^t

t = log(144/60)/log1.03

To find the value of t when z(t) equals 144, we need to set up an equation and solve for t. The given equation is:

z(t) = 60 * 1.03^t

We can substitute 144 in place of z(t):

144 = 60 * 1.03^t

Now, we need to isolate the exponential term by dividing both sides of the equation by 60:

144/60 = 1.03^t

Simplifying further, we get:

2.4 = 1.03^t

To solve for t, we need to take the logarithm of both sides of the equation. Let's take the natural logarithm (ln) of both sides:

ln(2.4) = ln(1.03^t)

Using the logarithmic property that ln(a^b) = b * ln(a), the equation becomes:

ln(2.4) = t * ln(1.03)

Now, divide both sides of the equation by ln(1.03) to isolate t:

t = ln(2.4) / ln(1.03)

Calculating this on a calculator, we find that t is approximately 10.479. Therefore, when z(t) equals 144, t is approximately 10.479.