The exponential growth formula is given by:

M = P * e^(rt)

where:
M is the final amount (325 grams in this case),
P is the initial amount (230 grams in this case),
r is the rate of growth (1.5% or 0.015 as a decimal), and
t is the time (in days, which we're trying to find).

First, we can substitute the known values into the equation:

325 = 230 * e^(0.015t)

Next, we can solve for e^(0.015t) by dividing both sides of the equation by 230:

e^(0.015t) = 325 / 230 = 1.41304348

Now, we can take the natural logarithm (ln) of both sides to solve for 0.015t:

ln(e^(0.015t)) = ln(1.41304348)

0.015t = ln(1.41304348)

Finally, we can solve for t by dividing both sides of the equation by 0.015:

t = ln(1.41304348) / 0.015

Using a calculator, we find that t ≈ 23.8 days.

Rounding to the nearest day, we get t = 24 days.

Question

The exponential growth formula is given by:

M = P * e^(rt)

where:
M is the final amount (325 grams in this case),
P is the initial amount (230 grams in this case),
r is the rate of growth (1.5% or 0.015 as a decimal), and
t is the time (in days, which we're trying to find).

First, we can substitute the known values into the equation:

325 = 230 * e^(0.015t)

Next, we can solve for e^(0.015t) by dividing both sides of the equation by 230:

e^(0.015t) = 325 / 230 = 1.41304348

Now, we can take the natural logarithm (ln) of both sides to solve for 0.015t:

ln(e^(0.015t)) = ln(1.41304348)

0.015t = ln(1.41304348)

Finally, we can solve for t by dividing both sides of the equation by 0.015:

t = ln(1.41304348) / 0.015

Using a calculator, we find that t ≈ 23.8 days.

Rounding to the nearest day, we get t = 24 days.

Knowee AI · Accepted Answer