Question

Bluefin tuna are large fish that can weigh 1,500 pounds and swim at speeds of 55 miles per hour. because they are used in sushi, a prime fish can be worth over $30,000. as a result, the western atlantic bluefin tuna have been exploited, and their numbers have declined exponentially. their numbers in thousands from 1974 to 1991 can be modeled by f (x) = 230(0.881)x, where x is the year and x = 0 corresponds to 1974. in what year were there or will there be 50 thousand tuna?

Answer 1

Given exponential function

f(x)= $230 (0.881)^x$

Where x is the number of years

f(x) is the number of tuna in thousands

To find out when number of tuna is 50 thousand , we plug in 50 for f(x) and solve for x

$50 = 230(0.881)^x$

Divide by 230 on both sides

$\frac{5}{23} = (0.881)^x$

Take ln on both sides

$ln(\frac{5}{23}) = ln(0.881)^x$

$ln(\frac{5}{23}) = x ln(0.881)$

Divide by ln(0.881) on both sides

x = $\frac{ln(\frac{5}{23})}{ln(0.881)}$

x= 12.04

Year = 1974 + 12.04 = 1986

so in 1986 there will be 50 thousand tuna.