Question

The population of a rare tropical rainforest bird has been changing exponentially. The initial estimation of the population was 800 birds with a decline per month, t, measured by the following function: B(t)= 800(0.65)^t/12 Choose the equivalent functions that represent the monthly percent change. Select all that apply.• B(t)=800(0.96)^t/12• B(t)=800(1-0.04)^t• B(t)=800(1+0.04)^t/12• B(t)=800(1-0.35)^t/12• B(t)=800(1+0.96)^t• B(t)=800(0.65)^t• B(t)=800(0.96)^t

Answer 1

Given the function:

$B(t)=800(0.65)^{\frac{t}{12}}$

if we look only at the growth factor with its exponent, we have:

$(0.65)^{\frac{t}{1}}=(\lbrack0.65\rbrack^{\frac{1}{12}})^t=(0.96)^t$

therefore, an equivalent expression that represent the monthly percent change is:/

$B(t)=800(0.96)^t$