Answer:
Step-by-step explanation:
The general formula for continuous exponential growth is A=A0•ert, where A0 is the initial amount, t is the elapsed time, and r is the rate of growth or decay. For this problem, r=0.005, so the formula is A=A0•e0.005t.
Since we want to know how long it takes of the amount to be 275% of the original amount, we can state that A=2.75A0. Substituting that into our formula gives us 2.75A0=A0•e0.005t. Dividing by A0 yields 2.75=e0.005t.
At this point we need to take the natural logarithm of both sides:
ln(2.75)=ln(e0005t)
ln(2.75)=0.005t
t=ln(2.75)/0.005, which is approximately equal to 202.3
We round up to 203 years.
The time it will take for the pride's population to reach 275% of its current size is 202 years.
Continuous compounding is the potentially endless number of periods in which compound interest may be calculated and reinvested into an account's balance.
[tex]A =Pe^{rt}[/tex]
where,
A is the principal amount after t number of years,
r is the rate at which the principal is been compounded, and P is the principal amount.
Given that the growth rate of the lion is 0.5% per year. Therefore, the time it will take for the pride to reach 275% of its current size is,
[tex]A =Pe^{rt}\\\\2.75P = Pe^{0.005 \times t}\\\\2.75 = e^{0.005 \times t}[/tex]
ln 2.75 = 0.005 × t
t = 202.32 ≈ 202
Hence, The time it will take for the pride's population to reach 275% of its current size is 202 years.
Learn more about Continuous Compound Interest:
https://brainly.com/question/24246899
#SPJ2
