Question

Find the exponential function that satisfies the given conditions: initial value = 70, decreasing at a rate of 0.5% per week

Answer 1

Answer:

Given: initial value ($A_{0}$)=70, and the rate of decreasing per week (r) =0.5%.

Consider the exponential function:

$A(t) = A_{0} \cdot (1 - r)^t$ ;

where A(t)= the value of the function at week t ,  $A_{0}$ = the initial value = 70 ,  r= rate of  the function is decreasing= 0.5% = 0.005 and t =  weeks.

Now,

$A(t) = A_{0} \cdot (1 - r)^t$

$A(t) = 70 \cdot (1-0.005)^t$

$A(t)=70(0.995)^t$.

The exponential function is, $A(t)=70(0.995)^t$.